Wow. What a long winding path that was! I had to repeat a few stretches but I reached the finish line and my brain is still inside my head so I'm okay. Thanks, Professor Eddie!
Something cool about your final answer...it’s a scaler of the conjugate of the original complex number, z. 1024 can be factored and that reveals the conjugate. Not sure why this result is obtained - coincidence or a message the problem’s authors are sending to the students of some deeper pattern. Cool.
Giving it a little deeper thought, because theta is 1/6 of the full circle (ie pi/3 or 360/6), the exponent works mod 6, and 1 and 11 are 1 and -1 mod 6 respectively, which may be the cause of ending up with a conjugate (scaled).
Thank you Eddie for the fantastic tutorial! Can somebody tell me what's going on at the Exponential : z = re * i(theta) ? What should I look up to undertstand that part?
where are they getting theta = pie/3 from? have they just memorised that or is there some logic they're using? i need a logical way of working it out coz my memory is just not that good.
It's easy to memorize. pi/3 means 60° cos60°=1/2 sin60°=√3/2 pi/6 means 30° cos30°=√3/2 sin30°=1/2 pi/4 means 45° con45°=1/√2 sin45°=1/√2 Or watch this video about special angles: th-cam.com/video/yJMGIKCVO-s/w-d-xo.html
@@mohammedal-musawi4820 haha. that would require me to remember the 60 deg values. no big deal. i can just accept that i need better memory. i always like backup plans to work stuff out if i forget. i'll try that video. cheers.
I took Calculus in Highschool and Multi Variable Calculus and Ddifferential Equations in College and never learned this. At least I do not remember learning this.
I guess you can get around writing "by de Moivre's Theorem" by just converting from polar to exponential form and back. Though then you need to write "by Euler's formula" two times, not sure that's better.
It is very through, but as an adult, I can follow that it is definitions but, student might be very confused.... on algebra, plus moturity and being able to concentrate on the topic.
Wow. What a long winding path that was! I had to repeat a few stretches but I reached the finish line and my brain is still inside my head so I'm okay.
Thanks, Professor Eddie!
Oh gosh, it's almost midnight and I'm watching an (amazing) video about de Moivre's Theorem...
Anyone who is reading this, I sincerely wish for you finding happiness in daily life, and you may be successful one day
We need more people like you in this world! I wish the same for you unknown friendly person!
w💫💫 back baby ‼️‼️
Thank you so much your the only video that has an updated teaching on this I might actually get an A or a B on my quiz thank you soooooo much.
Something cool about your final answer...it’s a scaler of the conjugate of the original complex number, z. 1024 can be factored and that reveals the conjugate. Not sure why this result is obtained - coincidence or a message the problem’s authors are sending to the students of some deeper pattern. Cool.
Giving it a little deeper thought, because theta is 1/6 of the full circle (ie pi/3 or 360/6), the exponent works mod 6, and 1 and 11 are 1 and -1 mod 6 respectively, which may be the cause of ending up with a conjugate (scaled).
Thank you Eddie for the fantastic tutorial!
Can somebody tell me what's going on at the Exponential : z = re * i(theta) ?
What should I look up to undertstand that part?
It's just another representation of complex number. For example z = a+bι = r(cosθ+ιsinθ) = re^{ιθ}
Is it pre calculus?
where are they getting theta = pie/3 from? have they just memorised that or is there some logic they're using? i need a logical way of working it out coz my memory is just not that good.
It's easy to memorize.
pi/3 means 60°
cos60°=1/2
sin60°=√3/2
pi/6 means 30°
cos30°=√3/2
sin30°=1/2
pi/4 means 45°
con45°=1/√2
sin45°=1/√2
Or watch this video about special angles: th-cam.com/video/yJMGIKCVO-s/w-d-xo.html
@@mohammedal-musawi4820 haha. that would require me to remember the 60 deg values. no big deal. i can just accept that i need better memory. i always like backup plans to work stuff out if i forget. i'll try that video. cheers.
@@mohammedal-musawi4820 ok, cool. that triangle certainly helps. just a few things to remember and i can work the rest out from there. thanks.
I took Calculus in Highschool and Multi Variable Calculus and Ddifferential Equations in College and never learned this. At least I do not remember learning this.
What grade is this??
I guess you can get around writing "by de Moivre's Theorem" by just converting from polar to exponential form and back. Though then you need to write "by Euler's formula" two times, not sure that's better.
It is very through, but as an adult, I can follow that it is definitions but, student might be very confused.... on algebra, plus moturity and being able to concentrate on the topic.
👍👍👍👏
Hiiii Eddie 🙌
This is how I kill time waiting on pizza delivery
Hey, I know that game! 😄
I've played 2048 too
what kinda high school teaches people this? one for geniuses?
In the UK this is covered in Further Maths A level, I guess the extension material in Australia is similar.