Compute the complex numbers, writing your answers in the standard form $a + bi$
a) $(1 + i)^{14}$
So I am trying to use polar coordinates and De Moirre's formula to compute this but I ran into a problem. I started out by writing it in the form:
$(r cis$$\theta$$)^{14}$ = $r^{14}$cis($14\theta$)
However, when solving for $r = \sqrt{x^2 + y^2}$ that would be $1 + i^2$ which would be $1 + (-1) = 0$. Unless I am missing something which would make my whole computation $0$.
I don't believe this is the case so I am just wondering if I am thinking about this technique incorrectly or if there is another way to go about this.
Thank you.
Update: With the help I've been able to come to an answer.
So I figured out 1 + i = $\sqrt{2}$cis($\frac{\pi}{4}$)
$(1 + i)^{14}$ = $\sqrt{2}^{14}$($\frac{\pi}{4}$ x 14) = $2^7$($\frac{\pi}{4}$ x 14)
$2^7$ cis($\frac{14\pi}{4}$) = $2^7$ (0 - 1i)
= 0 - 128i
If anyone can verify what I did, I would be appreciative.