First slide

Algebra of complex numbers

Question

The real part of $z = \frac{1}{1 - \cos θ + i \sin θ}$ is

Moderate

A

$\frac{1}{1 - \cos θ}$
B

$\frac{1}{2}$
C

$\frac{1}{2} \tan θ$
D

2

Solution

TIP
If $z = \frac{1}{ω},$ then
$Re (z) = \frac{Re (ω)}{| ω |^{2}}$
$\begin{array}{l} ∴ Re (z) = \frac{1 - \cos θ}{(1 - \cos θ)^{2} + \sin^{2} θ} \\ = \frac{1 - \cos θ}{1 - 2 \cos θ + \cos^{2} θ + \sin^{2} θ} \\ = \frac{1 - \cos θ}{2 (1 - \cos θ)} = \frac{1}{2} \end{array}$

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