Let a=Im(1+z^22iz), where z is any non-zero complex number.

Question

Let $a=\operatorname{Im}\left(\dfrac{1+z^2}{2iz}ight)$, where $z$ is any non-zero complex number. The set $A=\{a:|z|=1,\ z
e\pm1\}$ is equal to:

Accepted Answer

With $z=x+iy$, $|z|=1$: working through the algebra, $a=x$. Since $z
e\pm1$, $x\in(-1,1)$.

$A=(-1,1).$

Solutions · 1