Convert the given complex number in polar form: $1-i$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
Let the complex number be $z = 1-i$.
We represent $z$ in polar form as $z = r(\cos \theta + i \sin \theta)$,where $r \cos \theta = 1$ and $r \sin \theta = -1$.
Squaring and adding these equations,we get:
$r^2(\cos^2 \theta + \sin^2 \theta) = 1^2 + (-1)^2$
$r^2 = 2$
$r = \sqrt{2}$ (since $r > 0$).
Now,$\cos \theta = \frac{1}{\sqrt{2}}$ and $\sin \theta = -\frac{1}{\sqrt{2}}$.
Since $\cos \theta > 0$ and $\sin \theta < 0$,the angle $\theta$ lies in the $IV$ quadrant.
Thus,$\theta = -\frac{\pi}{4}$.
Therefore,the polar form is $\sqrt{2} \left[ \cos \left( -\frac{\pi}{4} \right) + i \sin \left( -\frac{\pi}{4} \right) \right]$.

Explore More

Similar Questions

If $Z = \frac{-2}{1 + \sqrt{3}i}$,where $i = \sqrt{-1}$,then the value of $\arg(Z)$ is

If the complex number $z = 2 - i(2 \tan \frac{5 \pi}{8})$ has modulus $r$ and argument $\theta$,then what are $(r, \theta)$?

If ${z_1}$ and ${z_2}$ are two non-zero complex numbers such that $|{z_1} + {z_2}| = |{z_1}| + |{z_2}|,$ then $\text{arg}({z_1}) - \text{arg}({z_2})$ is equal to

Let $z$ be a purely imaginary number such that $\text{Im}(z) < 0$. Then $\arg(z)$ is equal to

$arg\left( \frac{3 + i}{2 - i} + \frac{3 - i}{2 + i} \right)$ is equal to

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo