- Thread starter
- #1
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!
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!