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Complex Numbers

Overview: This article covers the definition of complex numbers of the form $$a+ bi$$ and how to graph complex numbers.

What are complex numbers?

A complex number can be written in the form a + bi where a and b are real numbers (including 0) and i is an imaginary number.

Therefore a complex number contains two 'parts':

• one that is real
• and another part that is imaginary

note: Even though complex have an imaginary part, there are actually many real life applications of these "imaginary" numbers including oscillating springs and electronics.

Examples of a complex number

$$\begin{array}{c|c} \blue 3 + \red 5 i & \\\hline \blue{12} + \red{\sqrt{-3}} & \red{\sqrt{-3}} \text{ is the } \blue{imaginary} \text{ part} \\\hline \blue 9 - \red i & \\\hline \blue{12} - \red{\sqrt{-25}} & \red{\sqrt{-25}} \text{ is the } \blue{imaginary} \text{ part} \\\hline \end{array}$$

How do you graph complex numbers?

Complex numbers are often represented on a complex number plane (which looks very similar to a Cartesian plane).

Practice Problems of complex number

Problem 2

This complex number is in the fourth quadrant.

Problem 3

This complex number is in the 2nd quadrant.

Problem 4

This complex number is in the 3rd quadrant.