`2/(1+costheta+isintheta)=?`

Convert the complex number Z in a+ib form if Z=1/(1-costheta-isintheta)

((1-sintheta+costheta)^(2))/((1+costheta)(1-sintheta))=?

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

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.

Prove that (frac(1+costheta+isintheta)(1+costheta-isintheta))^n=cos ntheta+isin ntheta .

If (3)/(2+costheta+isintheta)=a+ib"where"i=sqrt(-1)anda^(2)+b^(2)=lamdaa-3," the value of " lamda is

(cos3theta+isin3theta)^5/(costheta+isintheta)^6

Write the Argument of (1+sqrt3i)(costheta+isintheta)