Question

For a complex number $Z$ , if $arg\left(Z\right)\in \left(- \pi , \pi \right],$ then $arg\left\{1 + cos \frac{6 \pi }{7} + i sin ⁡ \frac{6 \pi }{7}\right\}$ is (here $i^{2}=-1$ )

• A. $\frac{3 \pi }{7}$
• B. $\frac{2 \pi }{7}$
• C. $-\frac{2 \pi }{7}$
• D. $-\frac{3 \pi }{7}$

Answer 1

Answer: (A)

Let $W=1+cos \frac{6 \pi }{7}+isin⁡\frac{6 \pi }{7}$ $=2cos \frac{3 \pi }{7}\left\{cos ⁡ \frac{3 \pi }{7} + i sin ⁡ \frac{3 \pi }{7}\right\}$
Hence, $arg\left(W\right)=\frac{3 \pi }{7}$