The argument of the complex number sin (6 π/5)+i(1+ cos (6 π/5)) is

Question

The argument of the complex number sin (6 π/5)+i(1+ cos (6 π/5)) is (A) (6 π/5) (B) (5 π/6) (C)  (9 π/10) (D) (2 π/5)

Tardigrade Admin · Accepted Answer

sin (6 π/5)+i(1+ cos (6 π/5)) =- sin (π/5)+i(1- cos (π/5)) =-2 sin (π/10) cos (π/10)+2 i sin 2 (π/10) =2 sin (π/10)(- cos (π/10)+i sin (π/10)) =2 sin (π/10)( cos (9 π/10)+i sin (9 π/10)) operatornameArg(z)=((9 π/10))

Q. The argument of the complex number $sin \frac{6 π}{5} + i (1 + cos \frac{6 π}{5})$ is

$\frac{6 π}{5}$

$\frac{5 π}{6}$

$\frac{9 π}{10}$

$\frac{2 π}{5}$

Q. The argument of the complex number sin56π​+i(1+cos56π​) is

56π​

65π​

109π​

52π​

sin56π​+i(1+cos56π​) =−sin5π​+i(1−cos5π​) =−2sin10π​cos10π​+2isin210π​ =2sin10π​(−cos10π​+isin10π​) =2sin10π​(cos109π​+isin109π​) Arg(z)=(109π​)

Q. The argument of the complex number $sin \frac{6 π}{5} + i (1 + cos \frac{6 π}{5})$ is

$\frac{6 π}{5}$

$\frac{5 π}{6}$

$\frac{9 π}{10}$

$\frac{2 π}{5}$