Question

The polar form of $(-1+i)$ is

• A. $\sqrt{2}(cos\pi /4+isin\pi /4)$
• B. $\sqrt{2}(cos5\pi /4+isin5\pi /4)$
• C. $\sqrt{2}(cos3\pi /4+isin3\pi /4)$
• D. $\sqrt{2}(cos\pi /4-isin\pi /4)$

Answer 1

The correct option is C $\sqrt{2}(cos3\pi /4+isin3\pi /4)$

Let $z=-1+i$

$r=|z|=\sqrt{1+1}=\sqrt{2}$

$\theta ={\tan }^{-1}\left(\frac{1}{-1}\right)=\frac{3\pi }{4}$

$\therefore -1+i=\sqrt{2}(\cos \frac{3\pi }{4}+i\sin \frac{3\pi }{4})$