Question

If the conjugate of a complex number $z$ is $\frac{1}{z - i}$, then $z$ can be:

• A. $i\left(\frac{1+\sqrt{5}}{2}\right)$
• B. $i\left(\frac{1-\sqrt{5}}{2}\right)$
• C. $\frac{1+i\sqrt{5}}{2}$
• D. $\frac{1-i\sqrt{5}}{2}$

Hint:

Since $|z|^2 - i\bar{z} = 1$ is real, $i\bar{z}$ must be real. This immediately implies that $\bar{z}$ (and thus $z$) has no real part and is purely imaginary, which eliminates options (C) and (D).

Answer 1

The Correct Option is A