I am embarrassed to ask this question. (complex) (1 Viewer)

[Wun_wun]

z= cos(theta) + isin(theta)
Express 1+z in modulus argument form. Hence show
(1+z)^4=16cos^4(theta/2)((Cos(2theta)+isin(2theta))

none of my methods seem to yield the result

 

[kooliskool]

Well, you know that:



So:






The trick to simplify this further is actually:




Hence:






Now the showing part:

 

[Wun_wun]

Kooliskool, that is where i got up to, I wasn't sure how to proceed from there, so i assumed i was using the wrong method.

 

[kooliskool]

check again, i actually found a way to do it right after i submitted the post lols

 

[Wun_wun]

Thanks

 

[kooliskool]

I guess the tricky part of this question is to look at what you are suppose to get, that's how I figured it out, I saw a half angle in the showing part, that gave me the idea of use the double angle on cos(\theta) to continue to simplify, which helps me solve the question in the end.

 

[Wun_wun]

That was a lot easier than i thought. The inverse tan was throwing me off. Thanks for helping bro!

 

[kooliskool]

You are welcome anytime , good luck with your studies and feel free to ask anything else, I will help when I have the time or a lot of other peoples here will too