How do you find conjugate of cos z?

To find the conjugate of ( \cos z ) for a complex number ( z = x + iy ) (where ( x ) and ( y ) are real numbers), you can use the formula for the cosine of a complex argument:

[ \cos z = \cos(x + iy) = \cos x \cosh y - i \sin x \sinh y. ]

The conjugate of ( \cos z ) is obtained by taking the complex conjugate of the expression, resulting in:

[ \overline{\cos z} = \cos x \cosh y + i \sin x \sinh y. ]