Adding Powers of 1 + i | Problem 221

[@scottleung9587]

I used a third method, in which I expressed 1+i in polar form and then used the unit circle to get the higher powers.

[@aplusbi]

Nice!

[@GreenMeansGOF]

Yup. When dealing with powers and roots, polar form is often very helpful.

[@jillerkore]

I thought of De-Moivre's theorem immediately after looking at the problem. Could easily generalize it to nth sum using the theorem

[@robin9740]

I used geometric series and then argument and modulus of the inner part to determine the argument and modulus of the higher powers. arg(z^n) = n*arg(z) and mod(z^n)=mod(z)^n

[@mcwulf25]

The 6th power is 8i

[@SidneiMV]

AP 😎