Question

Convert the following complex numbers into polar form.
$i(1+i)$

• A. $\sqrt{2}{e}^{i\frac{5\pi }{4}}$
• B. $\sqrt{2}{e}^{i\frac{\pi }{4}}$
• C. $\sqrt{2}{e}^{i\frac{3\pi }{4}}$
• D. $\sqrt{2}{e}^{i3\pi }$

Answer 1

The correct option is C $\sqrt{2}{e}^{i\frac{3\pi }{4}}$

$i(1+i)$

$=i+i^2$

$=i-1$

$=-1+i$

$=\sqrt{2}(-\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}})$

$\sqrt{2}\left(\cos \left(\frac{3\pi }{4}\right)\right)+$ $i\sin \left(\frac{3\pi }{4}\right)$

$\sqrt{2}e\frac{i3\pi }{4}$.