# Imaginary Numbers

### What Are Imaginary Numbers?

You will need to understand imaginary numbers for the ACT Math Test.

Imaginary numbers are not real numbers.

That is to say, imaginary numbers are not whole numbers, integers, decimals, or fractions.

You will need to know some basic laws of imaginary numbers for the exam, as well as how to perform some basic operations with imaginary numbers.

Consider the example questions on imaginary numbers below.

Question 1:

x and y are real numbers. ai and bi are imaginary numbers.

When does ai + x = bi + y ?

A. When a = b

B. When x = y

C. When a = x and b = y

D. When ai = y and bi = x

E. When ai = bi and x = y

Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.

Therefore, in order for ai + x to be equal to bi + y , ai must be equal to bi and x must be equal to y.

Question 2:

For the following equation, i represents an imaginary number. Simplify the equation:

(1 – i) – (3 – 2i)

A. –2 – 5i
B. –2 – i
C. –2 + i
D. –6 – 5i
E. –6 + i

To solve this type of problem, do the operation on the parentheses first.

(1 – i) – (3 – 2i) = 1 – i – 3 + 2i

Then group the real and imaginary numbers together in order to simplify and solve the problem.

1 – i – 3 + 2i =

1 – 3 – i + 2i =

–2 + i