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

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

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

Evaluate (costheta-isintheta)^n

Find (costheta+isintheta)^n

Express (1)/(1+cos theta-i sin theta) in the form of a+ib.

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 .

if |(2iz_1-z_1-z_2)/(2iz_1-z_1-z_2)|=|(costheta+ isintheta)/(costheta-isintheta)| then prove that z_1/z_2 is purely real.