Exam Study Radical Expressions and Complex Numbers

Closure of Sets Under the Four Basic Operations Real Numbers are closed under all operations. Irrational Numbers are not closed under the four basic operations. Rational Numbers are closed under the four basic operations. Integers are closed on all except division.

Radicals and Rational Exponents

Simplifying Radicals and Rational Exponents Examples:

Adding and Subtracting Radicals 1. Simplify all Radicals 2.Identify radicals with the SAME INDEX and SAME RADICAND. (only these can be combined) 3.For common radicals. Add/subtract the coefficients and KEEP THE COMMON RADICAL

Example:

Example

Multiplying Radicals

Example

Steps to Divide Radicals

Example:

I Pure Imaginary Numbers Imaginary Numbers Real Numbers

What is the definition of a complex number?

PowerAnswer

Adding and Subtracting Complex Numbers

Multiplying Complex Numbers

Identify: Real or Complex