Convert -1 + i into polar form: - Vidyadip

MCQ

Convert $-1 + i$ into polar form:

A
$\sqrt{2},\frac{5\pi}{4}$
✓
$\sqrt{2},\frac{3\pi}{4}$
C
$-\sqrt{2},\frac{\pi}{4}$
D
$\sqrt{2},\frac{\pi}{4}$

✓

Answer

Correct option: B.

$\sqrt{2},\frac{3\pi}{4}$

$\text{r}=\sqrt{\text{x}^2+\text{y}^2}=\sqrt{(-1)^2+\text{1}^2}=\sqrt{1+1}=\sqrt{2}$
$\text{r}\cos\theta = -1$ and $\text{r}\sin\theta = 1$
so, $\theta$ is in $2^{nd}$ quadrant since $\sin$ is positive and $\cos$ is negative.
$\tan\theta = -1$
$\Rightarrow \tan\theta =\frac{-\tan\pi}{4}$
$\Rightarrow\tan\theta=\tan(\frac{\pi-\pi}{4})=\frac{\tan3\pi}{4}$
$\Rightarrow\theta=\frac{3\pi}{4}$

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