Complex Numbers

You've studied complex numbers before - probably during your study of quadratic functions. Recall that: equation image indicator $LaTeX: i=\sqrt{-1},\:$ which means LaTeX: i^2=-1 .

Let's see how the complex number system fits in with other number systems. Notice in the image below that the real number system is a subset of the complex number system.

This image shows how the complex number system fits in with the other number systems such as real numbers, rational numbers, integers, and so forth.

In this lesson, we will revisit the definition of a complex number and will discuss how to add, subtract and multiply them.

We define a complex number as:

z = a + bi

z: the "name" of the number

a: the real part of the number

b: the coefficient of the imaginary part of the number

Let's review how to add and subtract complex numbers.

Example

Let z₁ = -3 + 4i and z₂ = 2 - 5i, find z₁ + z₂ and z₁ - z₂

Addition

Subtraction

z₁ + z₂ = (-3 + 4i) + (2 - 5i)

z₁ - z₂ = (-3 + 4i) - (2 - 5i)

Add the real parts and the imaginary parts

=(-3 + 2) + (4i - 5i)

=-1 -1i

Distribute the negative symbol, then combine like terms

= -3 + 4i - 2 + 5i

=(-3 - 2) + (4i + 5i)

=-5 + 9i

Let's practice multiplying complex numbers now - watch this video to review.

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