If a = (cosθ + i sinθ), prove that .

Given: a = cosθ + isinθ

To prove:

Taking LHS,

Putting the value of a, we get

We know that,

1 + cos2θ = 2cos²θ

or

and

Using the above two formulas

Using,

Rationalizing by multiply and divide by the conjugate of

Putting i² = -1, we get

We know that,

cos² θ + sin² θ = 1

= RHS

Hence Proved