Question

Number of solutions to the equation $z^2+|z{|}^2=0$ is

• A. $1$
• B. $2$
• C. $3$
• D. Infinitely many

Answer 1

Answer: (D)

Infinitely many

Let $z=x+iy$.

Given,

$z^2+|z{|}^2=0$

or, $z^2+z.\overline{z}=0$ [ Since $z.\overline{z}=|z{|}^2$]

or, $z(z+\overline{z})=0$

or, $z.2x=0$ [Since $z+\overline{z}=2x$]

or, $z=0$ or $x=0$.

Now $z=0$ gives a unique number but $x=0$ gives $z=iy$ for arbitrary $y$, in this case we get infinitely many solution.

So the given equation gives infinitely many solutions.