Polar form of a complex number
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Express the following in polar form
i) \(z=1+i\)
ii) \(z=1-\sqrt{3}i\)
$$
\begin{aligned}
\begin{aligned}\text{(i)}\quad Z &=1+i \\
r=& \sqrt{1+1} \\
=& \sqrt{2} \\
\tan \theta &=1 \\
\theta &=\frac{\pi}{4} \quad \text {( In 1st Quad) } \\
\therefore\ 2&=\sqrt{2} \operatorname{cis}\left(\frac{\pi}{4}\right)
\end{aligned}\\
\begin{aligned}\text{(ii)}\quad Z=& 1-\sqrt{3} i \\
r=& \sqrt{1+3} \\
=& 2 \\
\tan \theta &=-\frac{\sqrt{3}}{1} \quad \text { (4th quad) } \\
\theta &=-\frac{\pi}{3} \\ \therefore 2 &=2 \operatorname{cis}\left(-\frac{\pi}{3}\right) \end{aligned}
\end{aligned}
$$
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