# Phase Rotations

Learn how to rotate a complex number by using phases.

## We'll cover the following

Phase rotations impact a signal in a variety of ways. Therefore, understanding how a signal is rotated inphase is important for a DSP learner.

## Complex signals

In complex notation, rotating a complex number in the $IQ$ plane by a phase $\theta$ is very simple.

- For a number $V$ and phase $\theta$, we write a phase rotation as:

$W= V\cdot e^{j\theta}$

Since $e^{j\theta}$ is a complex number with magnitude 1 and phase $\theta$, the magnitude of the result $W$ stays constant while $\theta$ is added to the angle of that complex number.

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