Question

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

• A. $2$
• B. $4$
• C. $6$
• D. None of these

Answer 1

Answer: (A)

$2$

Let's assume that the given number z is of the complex form x+iy. Now |z| = $(x^2+y^2{)}^{\frac{1}{2}}$ and $x^2=0$ as square of the real part is zero.So This gives that $y^2=3$.Hence y can be either $+(3{)}^{\frac{1}{2}}or-(3{)}^{\frac{1}{2}}$ and so there are only 2 complex numbers possible which satisfy these conditions.