The real part of sinh `(alpha + I beta)` is

The imaginary part of cosh(alpha+i beta) is

The real part of |(cos alpha+isin alpha, cos beta+ i sin beta),(sin beta+i cos beta, sin alpha +icos alpha)| is

The real part of [[cos alpha+i sin alpha, cos beta+i sin beta],[ sin beta+i cos beta, sin alpha+i cos alpha]] is

The minimum value of the expression sin alpha + sin beta+ sin gamma , where alpha,beta,gamma are real numbers satisfying alpha+beta+gamma=pi is

The minimum value of the expression sin alpha + sin beta+ sin gamma , where alpha,beta,gamma are real numbers satisfying alpha+beta+gamma=pi is

The minimum value of the expression sin alpha + sin beta+ sin gamma , where alpha,beta,gamma are real numbers satisfying alpha+beta+gamma=pi is

The real part of determinant of [[cos + i sin alpha, cos beta + i sin beta],[sin beta + i cos beta, sin alpha + i cos alpha]] is

The minimum value of the expression sin alpha + sin beta+sin lambda , where alpha,beta,lambda are real numbers satisfying alpha + beta + lambda = pi is

Let alpha and beta be two distinct complex numbers, such that abs(alpha)=abs(beta) . If real part of alpha is positive and imaginary part of beta is negative, then the complex number (alpha+beta)//(alpha-beta) may be