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

Aug 28, 2016

In polar coordinates complex conjugate of $\left(r , \theta\right)$ is $\left(r , - \theta\right)$.

#### Explanation:

Let $w = x + j y$ be represented by $\left(r , \theta\right)$, then

$x + j y = r \cos \theta + j r \sin \theta$ or $x = r \cos \theta$ and $y = r \sin \theta$

As complex conjugate is $w \cdot = x - j y = r \cos \theta - j r \sin \theta$ or

= $r \cos \left(- \theta\right) + j r \sin \left(- \theta\right)$

Hence, in polar coordinates complex conjugate of $\left(r , \theta\right)$ is $\left(r , - \theta\right)$.