Convert `z=2/(1+costheta+isintheta)` in `a+ib` form

Convert Z=1/(costheta-isintheta) in a+ib form

Find (costheta+isintheta)^n

Convert the complex number (costheta+isintheta)^5 in a+ib form

Evaluate (costheta-isintheta)^n

Express 1/(1-costheta+2isintheta) in the form A+iB

Evaluate (costheta-isintheta)^(-n)

State true or false: If z= (cos2theta+isin2theta)/(costheta+isintheta) then z is unimodular.

"State whether True or False:" The complex number costheta+isintheta can be zero for some theta .

Let P denotes a complex number z=r(costheta+isintheta) on the Argand's plane, and Q denotes a complex number sqrt(2|z|^(2))(cos(theta+(pi)/(4))+isin(theta+(pi)/(4))) . If 'O' is the origin, then DeltaOPQ is

The argument of the complex number z=(1+i sqrt3)(1+i) (costheta+isintheta) is