- #1

kingwinner

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## Homework Statement

"This is an example from my textbook:

**Solve the equation z**

^{4}- 4z^{2}+ 4 - 2i = 0__Solution:__

Rearranging, we get z

^{4}- 4z

^{2}+ 4 = 2i

or (z

^{2}- 2)

^{2}= 2i = (1+i)

^{2}

This has solutions z

^{2}- 2 = 1+i or -1-i.

Equivalently z

^{2}=3+i or z

^{2}=1-i

These may be solved to give the 4 solutions of the original equation.

==========================

I don't understand the following step:

(z

^{2}- 2)

^{2}= (1+i)

^{2}=> z

^{2}- 2 = 1+i or -1-i

Why is this true? I remember for real numbers we have √(x

^{2}) = |x| (note that it is |x|, not x). Is this true for complex numbers? If so, then

(z

^{2}- 2)

^{2}= (1+i)

^{2}

=> z

^{2}- 2 = +/- √[(1+i)

^{2}] = +/- |1+i| ?

## Homework Equations

N/A

## The Attempt at a Solution

Shown above.

I hope someone can explain this. Any help is appreciated!

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