Question

The number of solutions of the equation z² + $\bar{z}$ = 0 is –

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (D)

4

Answer 2

Sol. On putting z = x + iy

we get x² – y² + 2ixy + x – iy = 0

Ž x² – y² + x = 0, y(2x – 1) = 0

Ž x = $\frac{1}{2}$ or y = 0

When x =$\frac{1}{2}$, y = ±$\frac{\sqrt{3}}{2}$

When y = 0, x = 0 or – 1

Ž System has four solutions