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

Let $z_{1}$ and $z_{2}$ be two complex numbers such that $\overline{z}_{1} = i \overline{z}_{2}$ and $\arg \left( \frac{z_{1}}{\overline{z}_{2}} \right) = \pi$. Then:

Let $z$ and $w$ be complex numbers such that $\overline{z} + i\overline{w} = 0$ and $\text{arg}(zw) = \pi$. Then $\text{arg}(z)$ equals

If $z_1=(2,-1)$ and $z_2=(6,3)$,then $\operatorname{amp}\left(\frac{z_1-z_2}{z_1+z_2}\right)=$

If $z = 1 - \cos \alpha + i \sin \alpha $,then $\text{amp } z$ =

Let $z$ satisfy $|z| = 1$ and $z = 1 - \bar{z}$.
Statement $1$: $z$ is a real number.
Statement $2$: The principal argument of $z$ is $\frac{\pi}{3}$.

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