The equation $z ¯ z + ¯ z + 10 = 0$ , represents

A circle

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

A parabola

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

An ellipse

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

A hyperbola

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

Open in App

Solution

The correct option is C A circle
Let $z = x + i y$
Then, $¯ z = x - i y$
Given, equation is as $z ¯ z + z + ¯ z + 10 = 0$
$\Rightarrow (x + i y) (x - i y) + (x + i y) + (x - i y) + 10 = 0$
$\Rightarrow x^{2} + y^{2} + 2 x + 10 = 0$
It represents the equation of a circle.

Suggest Corrections

Similar questions

z = x + i y

z ¯ z + 2 (z + ¯ z) + c = 0

If (1 + i)(z + $¯ ¯ ¯ z$ ) - i(a + i)(z - $¯ ¯ ¯ z$ ) + 2(a - 1)i = 0 and z $¯ ¯ ¯ z$ = 5 then the value of 'a' is

If z is a non-zero complex number, then $∣ ∣ ∣ \frac{| ¯ z |^{2}}{z ¯ z} ∣ ∣ ∣$ is equal to

z

∣ ∣ ∣ ∣ \frac{| ¯ z |^{2}}{z ¯ z} ∣ ∣ ∣ ∣

Find the equation of a circle whose centre is $z_{1}$ and radius r.

Join BYJU'S Learning Program