Question

The complex number 2(1 + i) can be represented in polar form as,

• A. $2\sqrt{2}{e}^{i\pi /4}$
• B. $\frac{\pi }{4}{e}^{i2\sqrt{2}}$
• C. $\sqrt{2}{e}^{i\pi /4}$
• D. $\frac{\pi }{4}{e}^{i\sqrt{2}}$

Answer 1

The correct option is A $2\sqrt{2}{e}^{i\pi /4}$

The complex number z can be represented in rectangular form as x + iy and in polar form as $r{e}^{i\varphi }$
$z=x+iy=r\cos \varphi +ir\sin \varphi =r{e}^{i\varphi }$

$where,r=|z|=\sqrt{x^2+y^2}=\sqrt{2^2+2^2}=2\sqrt{2}$
$and\varphi =ta{n}^{-1}\left(\frac{2}{2}\right)=\frac{\pi }{4}$

$Hence,z=2\sqrt{2}{e}^{i\pi /4}$