If `z=1+cos(pi/5)+isin(pi/5)` then `sin(argz)` is equal to

Options

A. `2cos""(pi)/(5)`
B. `2sin""(pi)/(10)`
C. `2cos""(pi)/(10)`
D. `2sin""(pi)/(10)`

Answer

C

Explanation

`|z|=sqrt(1^(2)+cos^(2)""(pi)/(5)+2cos""(pi)/(2)+sin^(2)""(pi)/(5))`
`=sqrt(1^(2)+1+2cos""(pi)/(2))=sqrt(2(1+cos""(pi)/(5)))`
`=sqrt(2(1+2cos^92)""(pi)/(10)-1))=sqrt(2(2cos^(2)""(pi)/(10)))=2cos""(pi)/(10)`