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Algebra II

Printable “Complex Numbers” worksheets:

Examples, solutions, videos, and worksheets to help Algebra II students learn how to rationalize complex numbers or simplifying complex number fractions.

There are four sets of rationalize complex numbers worksheets

- Rationalize Complex Numbers (Monomial ÷ Monomial)
- Rationalize Complex Numbers (Binomial ÷ Monomial)
- Rationalize Complex Numbers (Monomial ÷ Binomial)
- Rationalize Complex Numbers (Binomial ÷ Binomial)

Rationalizing complex numbers involves removing the imaginary part (usually represented as i) from the denominator of a complex number fraction or expression. This process is commonly used to simplify complex fractions or expressions with imaginary numbers. Here’s how to rationalize a complex number:

- Identify the Complex Denominator

Recognize that the denominator of the complex number fraction contains both real and imaginary parts. - Multiply by the Conjugate

Multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of a complex number in the form a + bi is a − bi. - Perform the Multiplication

Multiply the fraction by the conjugate in both the numerator and the denominator. This step ensures that you are not changing the value of the fraction because you are essentially multiplying it by 1. - Simplify

Simplify the resulting fraction by using distributive properties and combining like terms in both the numerator and the denominator. - Check for Further Simplification

In some cases, you may be able to simplify the expression further by identifying and canceling common factors in the numerator and the denominator.

Example:

Rationalize the complex number fraction (2+3i)/(4−5i)

- Identify the Complex Denominator.

The denominator is 4−5i, which contains both real and imaginary parts. - Multiply by the Conjugate.

The conjugate of 4−5i is 4+5i. - Perform the Multiplication.

Multiply both the numerator and the denominator by 4+5i: 4 Simplify.

Use the distributive property in the numerator and denominator:

Numerator: (2+3i)(4+5i) = 8 + 10i + 12i - 15 = -7 + 22i

Denominator: (4-5i)(4+5i) = 16 + 25 = 41

So, (2+3i)/(4−5i) = (-7+22i)/41

Have a look at this video if you need to review how to rationalize complex numbers.

Click on the following worksheet to get a printable pdf document.

Scroll down the page for more **Rationalize Complex Number Worksheets**.

**Printable**

(Answers on the second page.)

Rationalize Complex Number Worksheet #1 (Monomial ÷ Monomial)

Rationalize Complex Number Worksheet #2 (Binomial ÷ Monomial)

Rationalize Complex Number Worksheet #3 (Monomial ÷ Binomial)

Rationalize Complex Number Worksheet #4 (Binomial ÷ Binomial)

**Online**

Powers of i: Positive Exponents

Powers of i: Negative Exponents

Rationalize Complex Number Addition

Rationalize Complex Number Subtraction

Rationalize Complex Number Multiplication

Rationalize Complex Number Division

Rationalize Complex Number: Magnitude (Absolute Value)

Distance Between Two Rationalize Complex Numbers

Midpoint of Two Rationalize Complex Numbers)

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