Convert -1 - i into polar form: - Vidyadip

MCQ

Convert $-1 - i $ into polar form:

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

✓

Answer

Correct option: C.

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

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

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