Question

Find the number of solution of the equation $z^2$ + $|z{|}^2$ = 0.

• A. 2
• B. 4
• C. No solution
• D. Infinite

Answer 1

The correct option is D

Infinite

Solution: $z^2$ + $|z{|}^2$ = 0.

$z^2$ + $z\overline{z}$ = 0 {we know, $|z{|}^2$ = z $\overline{z}$}

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

Either z = 0 --------(I)

Or $z+\overline{z}$ = 0 --------------(II)

Let z = x + iy

$\overline{z}$ = x - iy

if z + $\overline{z}$ = 0

x + iy + x - iy = 0

2x = 0

x = 0

or

z = 0

x + iy = 0

z = 0 + iy

z = iy y $ϵ$ R ----------------(III)

Since, y belongs to all the real values.

From equation 3

We get, above equation has infinite number of solution.