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## Homework Statement

Show that (1+i) is a root of the equation z

^{4}=-4 and find the other roots in the form a+bi where (a) and (b) are real.

## Homework Equations

Using De Moivre's Theorem

z

^{n}=[r

^{n},nθ]

Modulus(absolute value of z) = 4

Argument = ???

## The Attempt at a Solution

r

^{4}=4 → r = (4)^(1/5)

argument(z) = ∏/4 (not sure if that was right....)

Let:

[r

^{4}],5θ] = [4,2n∏ + ∏/4]

and then solve for the solutions for (n=-1,-2,1,2...im assuming to make it symmetrical)