Question

Let \(z = \frac{a - \frac{i}{2}}{i - 2}\), where \(a\) is a real number and \(i = \sqrt{-1}\). If \(\text{Im}(z) = 0\), then the value of \(a\) is equal to

• A. 1
• B. 2
• C. 3
• D. 4
• E. 0

Hint:

If \(\frac{z_1}{z_2}\) is purely real, then \(z_1 \overline{z_2}\) is also purely real. You only need to set the imaginary part of the product of the numerator and the conjugate of the denominator to zero.

Answer 1

The Correct Option is A