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## Algebra 2

### Course: Algebra 2>Unit 2

Lesson 3: The complex plane

# Plotting numbers on the complex plane

Understand the roles of real and imaginary parts in forming coordinates. Learn how to plot complex numbers on a unique two-dimensional grid known as the complex plane. Discover the real and imaginary parts of complex numbers, and see how they correspond to the horizontal and vertical axes.  Created by Sal Khan.

## Video transcript

Move the orange dot to negative 2 plus 2i. So we have a complex number here. It has a real part, negative 2. It has an imaginary part, you have 2 times i. And what you see here is we're going to plot it on this two-dimensional grid, but it's not our traditional coordinate axes. In our traditional coordinate axis, you're plotting a real x value versus a real y-coordinate. Here on the horizontal axis, that's going to be the real part of our complex number. And our vertical axis is going to be the imaginary part. So in this example, this complex number, our real part is the negative 2 and then our imaginary part is a positive 2. And so that right over there in the complex plane is the point negative 2 plus 2i. Let's do a few more of these. So 5 plus 2i. Once again, real part is 5, imaginary part is 2, and we're done. Let's do two more of these. 1 plus 5i. 1-- that's the real part-- plus 5i right over that Im. All right, let's do one more of these. 4 minus 4i. Real part is 4, imaginary part is negative 4. And we're done.