Question

Number of solutions of the equation $z^3+\left[3{\left(\overline{z}\right)}^2\right]/\left|z\right|=0$ where z is a complex number is

• A. 2
• B. 3
• C. 6
• D. 5

Answer 1

The correct option is D 5

Give $z^3+\frac{3{\left(\overline{z}\right)}^2}{\left|z\right|}=0$
Let, z = ${re}^{i\theta }$
$⟹r^3{e}^{i3\theta }+{3re}^{-i2\theta }=0$
Since r cannot be zero, so ${re}^{i5\theta }=-3$,
Which will hold for r = 3 and five distinct values of $\theta$. Thus there are five solutions.