CSPE - Complex Numbers Lesson

Complex Numbers

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

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.

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.

 IMAGES CREATED BY GAVS