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#### Pranav

##### Well-known member

- Nov 4, 2013

- 428

**Problem:**

Let $z=x+iy$ satisfy $$z^2=z+|z^2|+\frac{2}{|z|^3}$$then the possible values of $x+y$ is

A)$-2^{1/4}$

B)$2^{1/4}$

C)$3^{1/4}$

D)$-5^{1/4}$

**Attempt:**

Substituting $z=x+iy$ is definitely not a good idea, it can be solved by substituting but since this is an exam problem, I believe that there is a much smarter way to solve the problem. But I am completely clueless about it. The $|z|^3$ factor in the denominator throws me off, I have absolutely no idea.

Any help is appreciated. Thanks!