Question

The principal value of arg z where $z=1+\cos \frac{6\pi }{5}+i\sin \frac{6\pi }{5}$ is given by

• A. $\frac{3\pi }{5}$
• B. $-\frac{\pi }{5}$
• C. $-\frac{3\pi }{5}$
• D. $\frac{\pi }{5}$

Answer 1

The correct option is A $\frac{3\pi }{5}$

$1+cos\frac{6\pi }{5}+isin\left(\frac{6\pi }{5}\right)$
$=2co{s}^2\frac{3\pi }{5}+i2sin\frac{3\pi }{5}.cos\frac{3\pi }{5}$
$=2cos\left(\frac{3\pi }{5}\right)[cos\frac{3\pi }{5}+isin\frac{3\pi }{5}]$
$=2cos\left(\frac{3\pi }{5}\right)[cos\frac{3\pi }{5}+isin\frac{3\pi }{5}]$ ....Since $\frac{3\pi }{5}$ is in the first quadrant.