SOLUTION: Find all non-zero complex number z satisfying z^2 + |z*| = 0. Here z* is complex conjugate of z.

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Question 998225: Find all non-zero complex number z satisfying z^2 + |z*| = 0. Here z* is complex conjugate of z.
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
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This equation has two solutions:

1)  z = i  (imaginary unit),     and

2)  z = -i.

There is no other solutions.

Check that these two are the solutions.

Think why there is no other solutions.