Question

Let $z_1\ne z_2\mathrm{and}\left|z_1\right|=\left|z_2\right|.$If $z_1$ has a positive real part and $z_2$ has negative imaginary part. Then, $\frac{z_2+z_1}{z_1-z_2}$ maybe

• A. $0$
• B. real and positive
• C. real and negative
• D. None of the above

Answer 1

The correct option is D

None of the above

Explanation for the correct option:

Determining if the numerator is purely imaginary and the denominator is purely real:

Given$z_1\ne z_2\mathrm{and}\left|z_1\right|=\left|z_2\right|$

The numerator is purely imaginary and the denominator is purely real.

$Im\left(z\right)andRe\left(z\right)$ are real numbers.

So, $\frac{z_2+z_1}{z_1-z_2}$ is purely imaginary.

Therefore, the correct answer is option (D).