Question
Write $1 - \text{i}$ in polar form.
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Answer
$\text{z}=1 - \text{i}$ $\text{r}=|\text{z}|$ $=\sqrt{1+1}$ $=\sqrt{2}$ Let $\tan\alpha=\Big|\frac{\text{Im(z)}}{\text{Re(z)}}\Big|$ $\therefore\tan\alpha=\Big|\frac{-1}{1}\Big|$ $=\frac{\pi}{4}$ $\Rightarrow\alpha=\frac{\pi}{4}$ Since point (1,−1) lies in the fourth quadrant, the argument of z is given by $\theta=-\alpha=-\frac{\pi}{4}$ Polar form $=\text{r}(\cos\theta+\text{i}\sin\theta)$ $\sqrt{2}\Big\{\cos\big(-\frac{\pi}{4}\big)+\text{i}\sin\big(-\frac{\pi}{4}\big)\Big\}$ $\sqrt{2}\big(\cos\frac{\pi}{4}-\text{i}\sin\frac{\pi}{4}\big)$
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