The equation $z^{2} + {¯ ¯ ¯ z}^{2} - 2 {| z |}^{2} + z + ¯ ¯ ¯ z = 0$ represents a

straight line

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

circle

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

hyperbola

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

parabola

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

Open in App

Solution

The correct option is B parabola
We have $z^{2} + {¯ ¯ ¯ z}^{2} - 2 {| z |}^{2} + z + ¯ ¯ ¯ z = 0$
Substitute $z = x + i y$
$\Rightarrow {(x + i y)}^{2} + {(x - i y)}^{2} - 2 (x^{2} + y^{2}) + x + i y + x - i y = 0$
$\Rightarrow 2 x^{2} + 2 {(i y)}^{2} - 2 x^{2} - 2 y^{2} + 2 x = 0$
$\Rightarrow - 4 y^{2} + 2 x = 0 \Rightarrow y^{2} = \frac{1}{2} x$
which is a parabola.

Suggest Corrections

Similar questions

z^{2} + z | z | + ∣ ∣ z^{2} ∣ ∣ = 0.

{| z - z_{1} |}^{2} + {| z - z_{2} |}^{2} = k, k \in R

z_{1} = 3 + 4 i

z_{2} = - 3 - 4 i

| z - z_{1} | + | z - z_{2} | = 10

∣ ∣ ∣ \frac{z - z_{1}}{z - z_{2}} ∣ ∣ ∣ = k

{| Z - Z_{1} |}_{1}^{2} + {| Z - Z_{2} |}_{2}^{2} = a

\frac{Z_{1} + Z_{2}}{2}

2 a \geq {| Z_{1} - Z_{2} |}_{1}^{2}

Join BYJU'S Learning Program