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**Homework Statement**

Find all complex solutions to

z^2 = z conjugate

i.e. (a+bi)^2 = a-bi

**The attempt at a solution**

__First attempt:__

factoring out (a+bi)^2 = a-bi

leads nowhere.

__Second attempt:__

r^2 (cos2v + isin2v) = r (cos-v + isin-v)

r must be 1.

2v = -v + 2∏n

3v = 2∏n

v= 2∏n/3

But that isn't the case.