### 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.

Our **download** will help you learn all of the skills you need for the real test.

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*

**The correct answer is E.**

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

**The correct answer is C.**

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

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