First slide

Geometry of complex numbers

Question

If $z = (λ + 3) - i \sqrt{5 - λ^{2}}$ , then the locus of z is

Moderate

A

ellipse
B

semicircle
C

parabola
D

straight line

Solution

Let z = x + iy. Then,
$x = λ + 3 and y = - \sqrt{5 - λ^{2}}$
$\Rightarrow (x - 3)^{2} = λ^{2}$ (1)
and $y^{2} = 5 - λ^{2}$ (2)
From Eqs. (1) and (2),
$(x - 3)^{2} = 5 - y^{2} or (x - 3)^{2} + y^{2} = 5$
Obviously it is a semicircle as y < 0. Hence, part of the circle lies below the x-axis.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App