- #1
kingwinner
- 1,270
- 0
Homework Statement
"This is an example from my textbook:
Solve the equation z4 - 4z2 + 4 - 2i = 0
Solution:
Rearranging, we get z4 - 4z2 + 4 = 2i
or (z2 - 2)2 = 2i = (1+i)2
This has solutions z2 - 2 = 1+i or -1-i.
Equivalently z2=3+i or z2=1-i
These may be solved to give the 4 solutions of the original equation.
==========================
I don't understand the following step:
(z2 - 2)2 = (1+i)2 => z2 - 2 = 1+i or -1-i
Why is this true? I remember for real numbers we have √(x2) = |x| (note that it is |x|, not x). Is this true for complex numbers? If so, then
(z2 - 2)2 = (1+i)2
=> z2 - 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!
Last edited: