For a complex number Z , if arg(Z)∈ (- π , π ], then arg 1 + cos (6 π /7) + i sin â¡ (6 π /7) is (here i2=-1 )

Question

For a complex number Z , if arg(Z)∈ (- π , π ], then arg 1 + cos (6 π /7) + i sin â¡ (6 π /7) is (here i2=-1 ) (A) (3 π /7) (B) (2 π /7) (C) -(2 π /7) (D) -(3 π /7)

Tardigrade Admin · Accepted Answer

Let W=1+cos (6 π /7)+isinâ¡(6 π /7) =2cos (3 π /7) cos â¡ (3 π /7) + i sin â¡ (3 π /7) Hence, arg(W)=(3 π /7)

Q. For a complex number $Z$ , if $a r g (Z) \in (- π, π],$ then $a r g {1 + cos \frac{6 π}{7} + i s in \frac{6 π}{7}}$ is (here $i^{2} = - 1$ )

$\frac{3 π}{7}$

$\frac{2 π}{7}$

$- \frac{2 π}{7}$

$- \frac{3 π}{7}$

Let $W = 1 + cos \frac{6 π}{7} + i s in \frac{6 π}{7}$ $= 2 cos \frac{3 π}{7} {cos \frac{3 π}{7} + i s in \frac{3 π}{7}}$
Hence, $a r g (W) = \frac{3 π}{7}$

Q. For a complex number Z , if arg(Z)∈(−π,π], then arg{1+cos76π​+isin⁡76π​} is (here i2=−1 )

73π​

72π​

−72π​

−73π​