The imaginary part of `( z-1) ( cos alpha - i sin alpha) + (z - 1)^(-1) (cos alpha - i sin alpha)` is zero then :

If the imaginary part of the complex number (z-1)(cos alpha-i sin alpha)+(z-1)^(-1)(cos alpha+i sin alpha) is zero,then which of the following options are correct? a) |z|=1 b) |z-1|=1 c) arg (z)=alpha d) arg (z-1)=alpha

Simplify the following. (Cos 5alpha + i Sin 5alpha) / (Cos alpha + i Sin alpha)

If (2sin alpha) / ({1 + cos alpha + sin alpha}) = y, then ({1-cos alpha + sin alpha}) / (1 + sin alpha) =

cos (n + 1) alpha cos (n-1) alpha + sin (n + 1) alpha sin (n-1) alpha =

Prove that, 1/3 ( cos^(3) alpha sin 3 alpha + sin^(3) alpha cos 3 alpha) = 1/4 sin 4 alpha

if [ ( cos alpha, - sin alpha),(sin alpha, cos alpha)] and A +A^1 =I then alpha =……

cos(n+1) alpha * cos(n-1)alpha + sin (n+1)alpha * sin (n-1) alpha =