Question

If \( z, \bar{z}, -z, -\bar{z} \) forms a rectangle of area \( 2\sqrt{3} \) square units, then one such \( z \) is:

• A. \( \frac{1}{2} + \sqrt{3}i \)
• B. \( \frac{\sqrt{5} + \sqrt{3}i}{4} \)
• C. \( \frac{3}{2} + \frac{\sqrt{3}i}{2} \)
• D. \( \frac{\sqrt{3} + \sqrt{11}i}{2} \)

Hint:

In problems involving rectangles formed by complex numbers, the vertices of the rectangle are represented by the complex number and its conjugate, as well as their negatives.