# Let z1 not equal to z2 and |z1| = |z2|. If z1 has positive real part and z2 has negative imaginary part. Then, (z2+z1)/(z1-z2) may be (1) 0 (2) real and positive (3) real and negative (4) None of the above

Solution:

Given z1 ≠ z2 and |z1| = |z2|

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

Im(z) and Re(z) are real numbers.

So (z2+z1)/(z1-z2) is purely imaginary.

Hence option (4) is the answer.