Prove that `alpha^(2)+beta^(2)=(alpha+beta)^(2)-2 alpha beta`

Find alpha^(2)+beta^(2)+alpha beta =?

Factorise alpha^2 +beta^2 + alpha beta

If alpha & beta are any two complex numbers, prove that |alpha+beta|^2+|alpha-beta|^2=2(|alpha|^2+|beta|^2)

Prove that: cos2 alpha cos2 beta+sin^(2)(alpha-beta)-sin^(2)(alpha+beta)=cos2(alpha+beta)

Prove that: cos2alpha\ cos2beta+sin^2(alpha-beta)-sin^2(alpha+beta)=cos2(alpha+beta) .

Prove that | alpha+sqrt(alpha^(2)-beta^(2))|+| alpha-sqrt(alpha^(2)-beta^(2))|=| alpha+beta|+| alpha-beta| where alpha,beta are complex numbers.

Prove that 2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(alpha+beta)=cos2 alpha

Prove that, gammaalpha ^ (2), beta ^ (2), gamma ^ (2) beta + alpha, gamma + alpha, alpha + beta] | = (beta-gamma) (gamma-alpha) (alpha-beta) ( alpha + beta + gamma)

Prove that cos^(2)(alpha-beta)+cos^(2)beta-2cos(alpha-beta)cosalphacosbeta is independent of beta .

Prove that sin^(2)alpha+cos^(2)(alpha+beta)+2sinalphasinbetacos(alpha+beta) is independent of alpha .