Yes, that's a separate topic. There might be different ways it could be done, but I would use De'Moivre's Theorem: convert the complex number to polar form, then sqaure root the modulus, divide the angle by 2, and voila, it's done. Then convert back to rectangular form. De'Moivre's Theorem gives a quick method for raising a complex number to a power, so realizing that a square root is a power of 1/2, that should work.
I'm using a lot of things - a graphics tablet, some screen capture software, and some video conversion software, and a headset. As far as I understand it, finding the square root of a complex number isn't so much a general formula as it is a procedure. So I can't give you a formula. I was thinking about making a video about the procedure, though, if I can find the time. D.O.
can you please explain how you calculated the square root of 3 - 4 i into (2-i) squared? i mean is there an easier way to calculated? I understand that (2-i) squared is equal to the square root of (3 - 4i) but what if i have huge numbers under the square root? how would you calculate it? i hope my question is clear and thank you again for your videos Mr Derekowens
I was wondering if you had any advice for me attempting the following: z^2-8z'+16=0 Where z is a complex number and z' is it's conjugate. Any help would be much appreciated, as I'm not sure how to use with the conjugate in there.
Solve the equation: Z^2+4Z +20+¡2(A+1)=0 where A is a constant has a complex conjugate root. If one of the conjugate root is of this quadratic is Z=B+2¡ ,where B is areal constant, find the possible values of A. This an assignment submitted July 3o please doings my dear dear
Basically, mathematicians define i that way, in order to make certain problems solvable. So i^2 = -1 by definition. Stated another way, i^2 = -1 because mathematicians have found that definition to be useful, but not because of any more fundamental reason.
@@derekowens Of course there is a fundamental reason, of which most humans are not aware of. It is deep rooted. You need to see it in terms of rotations in a 2 dimension plane ie complex plane. They are basically 2D numbers or lateral numbers. It is also defined in terms of magnitude and shift in phase angle (polar form). So does the same hold for quaternions and octonions.
Yes, that's a separate topic. There might be different ways it could be done, but I would use De'Moivre's Theorem: convert the complex number to polar form, then sqaure root the modulus, divide the angle by 2, and voila, it's done. Then convert back to rectangular form. De'Moivre's Theorem gives a quick method for raising a complex number to a power, so realizing that a square root is a power of 1/2, that should work.
Thanks Derek! Have an exam tomorrow about this topic.
I'm using a lot of things - a graphics tablet, some screen capture software, and some video conversion software, and a headset.
As far as I understand it, finding the square root of a complex number isn't so much a general formula as it is a procedure. So I can't give you a formula. I was thinking about making a video about the procedure, though, if I can find the time.
D.O.
You explain this very well.
@abhishekutkarsh Your comment interests me. Can you elaborate on that if you have time? Thanks, DO.
can you please explain how you calculated the square root of 3 - 4 i into (2-i) squared? i mean is there an easier way to calculated? I understand that (2-i) squared is equal to the square root of (3 - 4i) but what if i have huge numbers under the square root? how would you calculate it? i hope my question is clear and thank you again for your videos Mr Derekowens
Substitute: z=x+yi
and remember that Complex numbers can be equal only if their real and imaginary parts are equal
@@MK-cx5hb شكرا لك يا عزيزي بس سؤالي كان قبل سنوات ههههههه
@cool4ever1 يا اهلا وسهلا 😂😂😂، انتبهت لهذا لكن احتمال كبير انك مش انت الوحيد الي يبحث عن جواب لسؤالك لهيك كتبت جواب على كل حال
@@MK-cx5hb شكرا لك عزيزي اقدر لك تعاونك للغير. اتشرفت بالمحادثة معك اخوك ماجد من السعودية
@@cool4ever1 العفو والشرف لي
You can always write z as z = a + bi... if youre really patient.
I was wondering if you had any advice for me attempting the following:
z^2-8z'+16=0
Where z is a complex number and z' is it's conjugate.
Any help would be much appreciated, as I'm not sure how to use with the conjugate in there.
if z = a + bi, z'= a - bi (the reflection of the original z).
At the moment, i cannot help you more than this. Sorry.
@@Crazytesseract that’s alright, after 8 long years I finally solved it yesterday. Thank you though.
thanks but where is the video you explained how to the square root of complex numbers?
You can program this in a Casio fx-5800P, and you get quick answers. However you explain how it is done.
In simple quadratic equation , roots are points of intersection with -axis , What is the practical meaning of complex equation roots ?
how did find the 2-1 ??
Solve the equation: Z^2+4Z +20+¡2(A+1)=0 where A is a constant has a complex conjugate root. If one of the conjugate root is of this quadratic is Z=B+2¡ ,where B is areal constant, find the possible values of A. This an assignment submitted July 3o please doings my dear dear
how is i^2 = negative 1
Basically, mathematicians define i that way, in order to make certain problems solvable. So i^2 = -1 by definition. Stated another way, i^2 = -1 because mathematicians have found that definition to be useful, but not because of any more fundamental reason.
Because √-1 is equal to i, if you you sqaure i then you get -1. Think of it like this, √4 = 2 therefore 2² = 4
@@derekowens Of course there is a fundamental reason, of which most humans are not aware of. It is deep rooted.
You need to see it in terms of rotations in a 2 dimension plane ie complex plane. They are basically 2D numbers or lateral numbers. It is also defined in terms of magnitude and shift in phase angle (polar form).
So does the same hold for quaternions and octonions.
@@shanehart4967 √(-1) =±i.
Wait, if i is the square root of 1, can’t we just reference it as 1? - a grade 8 student
you probably could have used the second quadratic formula ( the one with b')