Need help in describing the set of complex numbers Let set $$C=\{z\in \mathbb{C}:\sqrt{2}|z|=(i-1)z\}$$ I think C is empty , because you could put it in this way$$|z|=-\frac{(1-i)z}{\sqrt{2}}$$ but would like a second opinion.

Hint: Set $z = Re^{i \theta}$. What can you say about $\theta$?

Alternative approach hint: Multiplication by $(i-1)$ is equivalent to what geometric transformation?
