# How to Solve the Complex Plane?

A complex number has both a real and an imaginary component and it cannot be plotted on a number line in the same way that real numbers can. The following step-by-step guide helps you learn how to graph complex numbers.

A complex number has both a real and an imaginary component. It’s the real part that has the number itself. The imaginary part, on the other hand, has the letter \(i\) attached to it. This imaginary \(i\) also has a mathematical definition. Imaginary number rule: \(?^2=−1\)

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## A step-by-step guide to graph the complex plane

Complex numbers cannot be plotted on a number line in the same way that real numbers can. We can still depict them graphically, though. To represent a complex number, we must consider both of its components.

As a way to represent the real and imaginary components of an object, we utilize a coordinate system known as a “complex plane”.

The complex numbers are positions on the plane represented as ordered pairs \((a, b)\), where \(a\) represents the horizontal axis coordinate and \(b\) represents the vertical axis coordinate.

**How to represent the components of a complex number on the complex plane?**

- Calculate the real and imaginary parts of the complex number.
- Show the real component of the number by moving down the horizontal axis.
- To reveal the imaginary component of the number, move parallel to the vertical axis.
- Make a diagram of the spot.

### The Complex Plane – Example 1:

Plot the complex number \(3+2i\).

This number has a real part of \(3\) and an imaginary part of \(2\).

### The Complex Plane – Example 2:

Plot the complex number \(1-4i\).

This number has a real part of \(1\) and an imaginary part of \(-4\).

## Exercises for the Complex Plane

### Graph these complex numbers.

- \(\color{blue}{-3+3.5i}\)

- \(\color{blue}{4-4i}\)

- \(\color{blue}{4-4i}\)

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