Question

Total number of complex numbers 'z', satisfying Re($z^2$) = 0, |z| = $\sqrt{3}$, is equal to :

• A. 2
• B. 4
• C. 6
• D. None

Answer 1

The correct option is B

4

Let z = x + iy, x, y, ∈ R. Then $z^2$ = $x^2$ - $y^2$ + ixy

Re($z^2$) = 0 $\Rightarrow$ $x^2$ = $y^2$ |z|= $\sqrt{3}$ $\to$ $x^2$ + $y^2$ = 3

∴ $x^2$ = $y^2$ = $\frac{3}{2}$ $\Rightarrow$ x = $\pm$$\sqrt{\frac{3}{2}}$, y = $\pm$$\sqrt{\frac{3}{2}}$.

Hence, there are four such complex numbers.