Number of solutions of the equation $| z |^{2} + 7 z = 0$ is

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2$
Let $z = x + i y$
Then, ${| z |}^{2} + 7 z = x^{2} + y^{2} + 7 (x + i y) = 0$
$\Rightarrow x^{2} + y^{2} + 7 x = 0$ & $7 y = 0$
$\Rightarrow x^{2} + 7 x = 0$ and $y = 0$
$\Rightarrow x = - 7 o r x = 0$ and $y = 0$
So, solutions are $z = - 7$ or $z = 0$
Hence, two solutions.

Suggest Corrections

Similar questions

3 x + 2 y = 1

4 x + 7 z = 1

x + y + z = 3

x - 2 y + 7 z = 0

L_{1} : \frac{x - 1}{2} = \frac{y}{- 2} = \frac{z + 2}{- 1}

L_{2} : \frac{x + 3}{8} = \frac{y - 4}{1} = \frac{z}{- 4}

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

λ

x + y + z = 6

4 x + λ y - λ z = λ - 2

3 x + 2 y - 4 z = - 5

λ

The number of solutions of the equation $z^{2}$ + $¯ z$ = 0 is

Join BYJU'S Learning Program