Question

The principal mod-amp form $2\sqrt{2}+i2\sqrt{2}$ is

• A. $2cis\frac{\pi }{4}$
• B. $\sqrt{2}cis\frac{\pi }{4}$
• C. $4cis\frac{\pi }{4}$
• D. $3\sqrt{3}cis\frac{\pi }{4}$

Answer 1

Answer: (C)

$4cis\frac{\pi }{4}$

Let $z=a+ib=2\sqrt{2}+2\sqrt{2}i$
$\therefore$ $\left|z\right|=\sqrt{a^2+b^2}$
$=\sqrt{8+8}$
$=4$
amp(z) $={\tan }^{-1}\left(b/a\right)$
$={\tan }^{-1}\left(1\right)$
$=\frac{\pi }{4}$