Question

What is the conjugate of the complex number `(r,theta)`, in polar form?

Answer 1

In polar coordinates complex conjugate of `(r,theta)` is `(r,-theta)`.

Explanation:

Let `w=x+jy` be represented by `(r,theta)`, then

`x+jy=rcostheta+jrsintheta` or `x=rcostheta` and `y=rsintheta`

As complex conjugate is `w*=x-jy=rcostheta-jrsintheta` or

= `rcos(-theta)+jrsin(-theta)`

Hence, in polar coordinates complex conjugate of `(r,theta)` is `(r,-theta)`.