Introduction to Complex Numbers

Complex numbers extend the real number system to include solutions to equations that have no real solutions.

The Imaginary Unit

Example: Simplifying Powers of

Complex Numbers

Example: Identifying Parts

Equality of Complex Numbers

Complex Plane

Modulus of a Complex Number

Example: Finding Modulus

Conjugate of a Complex Number

Example: Conjugate

Practice Problems

1. Simplify .

2. Find the real and imaginary parts of .

3. Find for .

4. Find the conjugate of and verify .