Sir please contact me i need your help seriously i've none to take advice since school teachers are not so much good and in my home my sister don't have time pls sir if you see my comment then don't ignore it this would very crucial help for me sir plssss...
𝐓𝐈𝐌𝐄𝐒𝐓𝐀𝐌𝐏𝐒 01:12 *Nature of Chapter* 03:00 Weightage 03:21 *Index* 05:50 Critical Topics 07:01 *Iota (i)* 07:55 *Powers of Iota* 14:39 *👁️🗨️bservation:* Sum of 4 consecutive terms of iota = 0 14:49 *Misconception* 16:53 *Describing Complex Number* 19:06 Real & Purely Imaginary Number 19:52 *Algebra of Complex Numbers* 20:12 ① Equality 20:39 *NOTE:* Inequality 21:15🥚Quadratic with complex coefficients 22:27🥚Complex Eqn gives 2 eqns of real terms 24:20 ② Addition & Substraction 25:17 ③ Multiplication 26:32 *NOTE* 27:03 *🧠 Remember:* (1 + i)² = 2i (1 - i)² = -2i 30:56 ④ Square Root 40:19 _Formula_ 40:42 ⑤ Division 44:30 Reciprocal or Multiplicative Inverse of a + ib 59:19 *Conjugate of Complex Number* 1:04:06 *🧠 Remember:* Values of zz̅ & z²+(z̅)² 1:13:52 *Properties of Conjugate* 1:15:48 _Imp Property_ 1:16:33 *⚡NOTE:* Property 6 is used a lot whenever we have to work around Re(z) or Im(z). 1:20:57 *REMARK:* If (x + iy)⁵ = p + iq then (y + ix)⁵ = q + ip 1:21:25 Questions based on Property 6 1:34:30 *Argand Plane* 1:35:31 *Modulus and Argument* 1:36:25 Modulus of Complex Numbers (|z|) 1:36:42 Argument of Complex Numbers (arg(z)) 1:43:57 *NOTE:* Principle Argument 1:45:13 *NOTE:* General Argument 1:46:44 *⚡NOTE:* Argument of Real & Purely Imaginary Number 1:47:45 arg(0) = Not Defined 1:48:00 _Good Question 🚩_ 1:54:33 _Question involving Re = 0 or Im = 0_ 2:00:50 *Properties of Modulus* 2:02:04 Triangle Inequality 2:03:44 Questions on Properties ②③④ 2:06:23 _🥚Solving Cubic Complex equation_ 2:12:11🥚Another Approach to solve questions where Re=0 or Im=0 info is given 2:14:07 _🥚Creating desired form_ 2:17:40 *Questions on Property ⑤* 2:19:45 _🥚If mod is there but don't know what to do_ 2:23:36 _Good Question_ 2:27:57 *RESULT:* |z₁+z₂|² & |z₁-z₂|² 2:30:54 *⚡RESULT:* Conjugates in addition or reciprocals in addition inside MOD 2:31:12 *🌟 NOTE:* When value of |z| given 2:34:19 *Standard Variety of Question 🚩* 2:41:35 *Triangle Inequality* 2:52:56 _Different Variety (z in denominator)_ 2:55:35 _Best Variety of Question 🚩_ 2:58:12 *Properties of Argument* 2:59:34 *👁️🗨️bservation* 3:04:46 _Good Question 🚩_ 3:08:36 *Representation of Complex Numbers in different forms* 3:10:19 *NOTE* 3:10:30 Application of Polar Form 3:13:00 2ⁿᵈ Application of Polar Form 3:18:05 Application of Euler Form 3:25:17 *De-Moivre’s Theorem* 3:29:39 _Difficult Question 🏴☠️_ 3:34:27 *Cube Roots of Unity* 3:36:00 *Properties of ω* 3:38:07 *⚡REMARK:* Roots of z² ± z +1 3:38:39 *👁️🗨️bservation:* Plotting Cube Roots 3:43:59 Common Mistake❗ 3:58:12 Standard Question 4:03:22 *Few identities involving Omega*
Significance of i : 7:10 ( i kabhi dikhega nhi, bas ye dimaag mein rkhna h ki i = √-1 ) 🌟 Std step 1) 1:00:56 1:02:05 write z = x + iy (z nikalna ho from eqn, use this) OR. 2) 21:5531:2936:52 (make out that the result/answer is a CN, say z which is = x + iy) 🌟 22:2623:3731:3936:591:52:58 : in CN, 1 eqn gives two info (1st by comparing real part on both sides, 2nd by comparing imaginary part on both sides) Imp Variety Q in Conjugate of CN : 1:00:37. (Put z = x + iy and then obtaining 2 info from 1 eqn) 1:15:05 1:19:02 1:19:56 : Conjugate mein power andar bahar ja skti h Method to use info that CN (say z) is purely imaginary or real : 1:22:33 1:26:05 1:27:43 1:32:38 1:55:30 (z aur zconj. ka addn aur subtraction yaad kro and use accordingly as per q) 1:29:55. : Also use this property to comment upon Re(z) or Im(z) {har baar 0 ho, zaroori thodi h} 2:09:22 2:15:26 : Solving Tip - Aese q mein ek side bnane ki koshish kro, doosri side apne apne bn jaegi ( for eg here we created RHS by taking mod and sq in given eqn) 🌟 ie desired cheez ko create kro!!! 2:06:32 : Cubic in z - Find 1 root by hit and trial (like we used to do in a cubic in x) by putting values = i, -i etc. 2:16:05 : MOD chahiye toh mod apply kro ( to get eqn in |z| ) 2:18:46 2:20:15 2:22:05 2:28:17: 1) Jab bhi MOD ke andar z baitha ho, sq it and use (z.zconj = |z|²). 2) MOD baitha h aur kuch smjh nhi aa rha, Sq it and use (|z|² = z.zconj) 2:31:42 2:32:23 2:34:47 2:35:45 : MOD ki value given ho (let |z| = a) , toh use (z.zconj = a²) anyhow in asked expn 3:10:34 3:12:48 : Polar Form : |z|, theta pta h then we can write CN
0:00 Introduction & Nature of Chapter 3:21 Index and Critical topics 7:01 Iota & Powers of Iota 16:53 Describing complex numbers & its Algebra 55:54 Conjugate of complex numbers 1:34:30 Argand Plane (Modulus and Argument) 2:00:49 Properties of modulus 2:58:07 Properties of Argument 3:08:26 Representation of complex numbers in different forms 3:25:17 DE-Moivre' Theorem 3:34:21 Cube roots of Unity
THANKS ALOT SIR!!! I am OVERWHELMED by the way you teach ALL the concepts including ADV. LEVEL with such an ease, it directly goes in head! Literally I feel you are one of THE BEST MATHEMATICS TEACHERS in INDIA. MERA BHAI MERA BHAI 🔥. You made it easy for me to enjoy learning.
Sir at 1:07:20 .. We're getting x=+2 or -2 and y +1 or -1... But sir since we're using "X*Y=15"..doesn't that mean that X and Y need to have the same sign? And doesn't that also ultimately mean that x and y also need to have the same sign.... So aren't possible solutions for this equation (2,1) and (-2,-1)? So the answer should be D(2) right?
@@aaravbaid6164 I didn't wanna type the entire "(x²+y²)(x²-y²) so I substituted that with capital X and capital Y. If sir had seen this message he'd have understood But thanks to your comment I've realised my silly mistake. It'll be too complicated to explain what mistake exactly I made through TH-cam comments, but yeah I figured out what I was doing wrong. My mistake isn't what you think it is, it's something different.
@@aaravbaid6164 exactly..they're squared so they can be both +-2 and +-1..i missed the square part when i originally solved this..that's kinda the silly mistake hahah
1:54:36 Method -4 put z = i y ( iota* y) and then rationalize and put imaginary part equal to zero the we got answer...Plz do it in smart way it`s not a lengthy method
They have given the value 1 just we have to find value for which iota will be 1 so i^4 = 1 and they sir equated value of m and n directly the hcf of both..
The PDF of the session is in the link pinned in the telegram channel t.me/JEEnexus
Hii sir I am your big fan 🎉🎉🎉
Sir please contact me i need your help seriously i've none to take advice since school teachers are not so much good and in my home my sister don't have time pls sir if you see my comment then don't ignore it this would very crucial help for me sir plssss...
bhaiya thoda or detail me explain Karo pls pls pls bhaiya thoda week hu kuch kuch chize samaj nahi ata
@@passionaticmusicbyvansh1838 how sir will contact you
Add some way he can contact you 🤔
Bhai please today sa aur gehrai me explain karo meko samajh me nahi aata jaldi bahot week hu padhne me please bhaiyya please😔😔🥺
𝐓𝐈𝐌𝐄𝐒𝐓𝐀𝐌𝐏𝐒
01:12 *Nature of Chapter*
03:00 Weightage
03:21 *Index*
05:50 Critical Topics
07:01 *Iota (i)*
07:55 *Powers of Iota*
14:39 *👁️🗨️bservation:* Sum of 4 consecutive terms of iota = 0
14:49 *Misconception*
16:53 *Describing Complex Number*
19:06 Real & Purely Imaginary Number
19:52 *Algebra of Complex Numbers*
20:12 ① Equality
20:39 *NOTE:* Inequality
21:15🥚Quadratic with complex coefficients
22:27🥚Complex Eqn gives 2 eqns of real terms
24:20 ② Addition & Substraction
25:17 ③ Multiplication
26:32 *NOTE*
27:03 *🧠 Remember:* (1 + i)² = 2i
(1 - i)² = -2i
30:56 ④ Square Root
40:19 _Formula_
40:42 ⑤ Division
44:30 Reciprocal or Multiplicative Inverse of a + ib
59:19 *Conjugate of Complex Number*
1:04:06 *🧠 Remember:* Values of zz̅ & z²+(z̅)²
1:13:52 *Properties of Conjugate*
1:15:48 _Imp Property_
1:16:33 *⚡NOTE:* Property 6 is used a lot whenever we have to work around Re(z) or Im(z).
1:20:57 *REMARK:* If (x + iy)⁵ = p + iq
then (y + ix)⁵ = q + ip
1:21:25 Questions based on Property 6
1:34:30 *Argand Plane*
1:35:31 *Modulus and Argument*
1:36:25 Modulus of Complex Numbers (|z|)
1:36:42 Argument of Complex Numbers (arg(z))
1:43:57 *NOTE:* Principle Argument
1:45:13 *NOTE:* General Argument
1:46:44 *⚡NOTE:* Argument of Real & Purely Imaginary Number
1:47:45 arg(0) = Not Defined
1:48:00 _Good Question 🚩_
1:54:33 _Question involving Re = 0 or Im = 0_
2:00:50 *Properties of Modulus*
2:02:04 Triangle Inequality
2:03:44 Questions on Properties ②③④
2:06:23 _🥚Solving Cubic Complex equation_
2:12:11🥚Another Approach to solve questions where Re=0 or Im=0 info is given
2:14:07 _🥚Creating desired form_
2:17:40 *Questions on Property ⑤*
2:19:45 _🥚If mod is there but don't know what to do_
2:23:36 _Good Question_
2:27:57 *RESULT:* |z₁+z₂|² & |z₁-z₂|²
2:30:54 *⚡RESULT:* Conjugates in addition or reciprocals in addition inside MOD
2:31:12 *🌟 NOTE:* When value of |z| given
2:34:19 *Standard Variety of Question 🚩*
2:41:35 *Triangle Inequality*
2:52:56 _Different Variety (z in denominator)_
2:55:35 _Best Variety of Question 🚩_
2:58:12 *Properties of Argument*
2:59:34 *👁️🗨️bservation*
3:04:46 _Good Question 🚩_
3:08:36 *Representation of Complex Numbers in different forms*
3:10:19 *NOTE*
3:10:30 Application of Polar Form
3:13:00 2ⁿᵈ Application of Polar Form
3:18:05 Application of Euler Form
3:25:17 *De-Moivre’s Theorem*
3:29:39 _Difficult Question 🏴☠️_
3:34:27 *Cube Roots of Unity*
3:36:00 *Properties of ω*
3:38:07 *⚡REMARK:* Roots of z² ± z +1
3:38:39 *👁️🗨️bservation:* Plotting Cube Roots
3:43:59 Common Mistake❗
3:58:12 Standard Question
4:03:22 *Few identities involving Omega*
Thank you bro ❤❤
Means alot 🙌
Thanks but lec ended late here💀💀
Is it just me who needs 7-8 hrs to complete a 4 hr lecture?
u r sincere thats why
You are not the only one I will take 2 days to complete lecture 😂😂😂😅
Yes
Me also
4 dys still not complete
No argument ,
Arvind sir One shot lectures are top notch. ❤️🗿
❤❤
Yes bro No tan^-|y/x|, I also agree with you
Sameer chincolikar sir☠️☠️ vo to complex ka unka he nhi isliye yaha ana pada varna unke one shot ka koi comparison nhi ha
Significance of i : 7:10 ( i kabhi dikhega nhi, bas ye dimaag mein rkhna h ki i = √-1 )
🌟 Std step
1) 1:00:56 1:02:05 write z = x + iy (z nikalna ho from eqn, use this)
OR.
2) 21:55 31:29 36:52 (make out that the result/answer is a CN, say z which is = x + iy)
🌟 22:26 23:37 31:39 36:59 1:52:58 : in CN, 1 eqn gives two info (1st by comparing real part on both sides, 2nd by comparing imaginary part on both sides)
Imp Variety Q in Conjugate of CN : 1:00:37. (Put z = x + iy and then obtaining 2 info from 1 eqn)
1:15:05 1:19:02 1:19:56 : Conjugate mein power andar bahar ja skti h
Method to use info that CN (say z) is purely imaginary or real : 1:22:33 1:26:05 1:27:43 1:32:38 1:55:30 (z aur zconj. ka addn aur subtraction yaad kro and use accordingly as per q)
1:29:55. : Also use this property to comment upon Re(z) or Im(z) {har baar 0 ho, zaroori thodi h}
2:09:22 2:15:26 : Solving Tip - Aese q mein ek side bnane ki koshish kro, doosri side apne apne bn jaegi ( for eg here we created RHS by taking mod and sq in given eqn) 🌟 ie desired cheez ko create kro!!!
2:06:32 : Cubic in z - Find 1 root by hit and trial (like we used to do in a cubic in x) by putting values = i, -i etc.
2:16:05 : MOD chahiye toh mod apply kro ( to get eqn in |z| )
2:18:46 2:20:15 2:22:05 2:28:17:
1) Jab bhi MOD ke andar z baitha ho, sq it and use (z.zconj = |z|²).
2) MOD baitha h aur kuch smjh nhi aa rha, Sq it and use (|z|² = z.zconj)
2:31:42 2:32:23 2:34:47 2:35:45 : MOD ki value given ho (let |z| = a) , toh use (z.zconj = a²) anyhow in asked expn
3:10:34 3:12:48 : Polar Form : |z|, theta pta h then we can write CN
Dhanywad bhai 🙏
0:00 Introduction & Nature of Chapter
3:21 Index and Critical topics
7:01 Iota & Powers of Iota
16:53 Describing complex numbers & its Algebra
55:54 Conjugate of complex numbers
1:34:30 Argand Plane (Modulus and Argument)
2:00:49 Properties of modulus
2:58:07 Properties of Argument
3:08:26 Representation of complex numbers in different forms
3:25:17 DE-Moivre' Theorem
3:34:21 Cube roots of Unity
1:21:20 done nd dusted 1 take conjugate on both side 2 multiply i^5 in both the side nd simplify get the ans
Thx
THANKS ALOT SIR!!! I am OVERWHELMED by the way you teach ALL the concepts including ADV. LEVEL with such an ease, it directly goes in head! Literally I feel you are one of THE BEST MATHEMATICS TEACHERS in INDIA. MERA BHAI MERA BHAI 🔥. You made it easy for me to enjoy learning.
Starting the lecture
Will complete with repetition aur sheet by tomorrow evening
Thankyou bhai ❤❤❤
Completed
Sir iske baad sequence and series one shot kijiye na please 🥺🥺
Like to get cs in iit bombay😂😂😂
😂
Iti bombay😂😂😂
Yes
Four like congratulations 🎉@Hhuubhgyh
Ya ofcourse chacha hi to IIT ka paper banate h tumhare
Best math teacher i can confirm !!
Sir please take one shot of sequence and Series
everything done and dusted , amazing lecture very easily explained...🥰
Sir Remark✅ , questions in between✅ and worksheet ✅ basically everything done and dusted 👍 . Thank you bhai. ♥️
😂😂😂
Hasa kyu be@@Fhkdutdfhkorhfjg
copied from jee nexus comments🙂
😂😂😂
Yeah crystal clear
Mera bhai 😊😊😊❤❤❤❤❤❤
Unimodular question done and dusted sir❤❤❤❤.......ans is 2
Commerce with math students will like❤️
Lets everyone say KNOCK. KNOCK KAUN AAYA ,MERA BHAI AAYA ❤
Knock knock knock, kaun aaya , mera backlog mate aaya 😂😂
bc padh le ye sab naa krke
Tu kaun hai jo mujhe saste advices de raha hai 😂😆
@@JEEADVANCED2025-ej5zj bhai sahi me padh le
Sir please sequence and series
1 subscribe = under 2k rank in jee advanced ❤❤❤❤❤😊😊😊😊😊
Bro if u get more than 2k subscribers then how will it be possible
@user-xy9pd4mh5i 💀
44:20 smile 🙂🙂🙂🙂😊😊
1:21:02 remark done and dusted
Can you tell me the approch to prove this like where to start
1:24:41 sir 1 ke jagah (alpha)(alpha) conjugate rakh dete to calculation nhi karna padta direct answer aata
1:21:36
Remark: Done and Dusted
How did you do it?
East or west arvind Kalia sir is the best ❤🎉
Really awesome ❤
2:23:34 Unimodular wala question done and dusted.
Can you tell me the answer?
@@BlackSpadeZ 2
Relation and functions plz sirrrr
yes sir
Sir bada mod wala question done and dusted by method 3😊😊😊😊
Watching this for straight 4 hours, I became a subscriber of this channel as well as a permanent disciple of the teacher..
U are the best bhai
Unimodular wala question done and dusted 😊
2:17:35
Sir didn't ask but still I dropped the banger
Done and l Dusted😎
For self
1:54:34 adv problem
Sir at 1:07:20 .. We're getting x=+2 or -2 and y +1 or -1... But sir since we're using "X*Y=15"..doesn't that mean that X and Y need to have the same sign? And doesn't that also ultimately mean that x and y also need to have the same sign.... So aren't possible solutions for this equation (2,1) and (-2,-1)? So the answer should be D(2) right?
Where did we use that X*Y=15 ??
@@aaravbaid6164 I didn't wanna type the entire "(x²+y²)(x²-y²) so I substituted that with capital X and capital Y. If sir had seen this message he'd have understood
But thanks to your comment I've realised my silly mistake. It'll be too complicated to explain what mistake exactly I made through TH-cam comments, but yeah I figured out what I was doing wrong. My mistake isn't what you think it is, it's something different.
@@joshuabell1133 Yeah both your substitution as 'X' and 'Y' are both positive when x= ±2 and y = ±1 due to being squared in 'X' and 'Y'
@@aaravbaid6164 exactly..they're squared so they can be both +-2 and +-1..i missed the square part when i originally solved this..that's kinda the silly mistake hahah
1:54:36 Method -4 put z = i y ( iota* y) and then rationalize and put imaginary part equal to zero the we got answer...Plz do it in smart way it`s not a lengthy method
How can you say that Z is purely imaginary??
Sir PLEASE bring class 12 calculus
52:41 Sir isme toh cross multiply se hi kaam ban jaata, otherwise toh power 4 ki equation solve karni padti hai
1:21:02
by using binomial
Thanks sir Aap hame free pada rahe hai❤❤
7:01 lecture starts
Thank you
sir nahi ❌ bhai✔
Unimodular Q done and dusted❤
Very good video sir , best explanation , a suggestion: give us some time to make notes
Sq root formula
Reciprocal is multiplicative inverse
1:21:10 Remark Done And Dusted🫡
How
You made my journey easy with this chapter.
Thankx BHAI ❤
3:19:33 note there will be+i√3/2
1:21:20 question is done and dusted
Thanks sir❤❤❤❤
Thankyou sm sir😊
4:01:40 how did alpha^2021 = alpha from alpha^5=1?
Sir answer is, x=-4+-√73/16
Sirji done and dusted ❤
Bada sa question done (modulus z² wala) and tested and by myself without method 1,2,3
All hw questions are done and dusted sirr
From Bangladesh Sir. Big fan❤❤
advance wala badiya question done and dusted(calculation wala)
Thank you 😊
1:13:39
Advance wala badiya Q done and dusted
2:00:32 Done and Dusted!!!!
Best teacher
2:23:13 unimodular qs done and dusted 🫡
Sir 2:13 Wale Q me agar componendo dividendo lege to 4 aayega
Sir bhagwan ke liye agla chapter snp le aao sirrr aapki bhot kripa rahegi 🙏🙏🙏🙏
Kiya bola tumne siiiiirrrr arvind bhaiya ab bhai nahi raheee sir ho gaay haa
Sno mtlb ??
@@Guru-mf3ew snp matlab sequence and progressions. Different coachings me different naam se bolte hai
43:17 divide me toh 5 tha?
done and dusted
unimodular ques done and dusted!
3:16:18 that's my name Debasish
3:27:51 here aswell
3:04:45
Unimodular wala done and understad
Sir at 30:00 can n be 0 , if not then why
Positive integer bola he
unimodular question done and dusted! on 21-08-2024
1:08:59 ❤
What a minute it reminds me something
sir jaldi se sabhi chapter ke one shot daal dijiye Nov tak
syllabus Pura revise bhi karna hai
2:23:34 unimodular wala question done and dusted
ans 4 ??
Sir please relation and function ka session le aaye
Sir ur camera becoming blurr....😢
Mod ka bada question done and dusted
Sir physics ke lecture kb ayenge class 12 ke
21:15
1:54:32
2:02:04
Is there any another part of complex number
Is any other vdo of complex number
Sir plz take pyqs session on complex no.s
2:13:55 can't we use Componendo and dividendo here
Y ki value pata nahi hai
unimodular question done and dusted
Sir Complex number conjugate wala calculation done and dusted
REPEAT
48:30
1:06:00
1:13:05
2:13:00
48:42 I didn't understand the logic followed here, someone explain please.
They have given the value 1 just we have to find value for which iota will be 1 so i^4 = 1 and they sir equated value of m and n directly the hcf of both..
@@treyjaiswal1428 Thank you so much!! This question was on my unsolvable list but I can try it again now.
unimodular wala question done and dusted bhai!
Sir unimodular Waala question done and dusted
unimodular done and dusted
Sir Revision+Sheet Done and Dusted
Can somebody explain the question at 2:47:05
Not to Brag abt it But i study from A Math Legend 💎💎
thank u sir
Is this from basic !?
No
yes but it is fast as sir does not repeat anything again so we listen again by going backward so it takes a lot of time
1:46:02😂😂😂