Complex Numbers

Definition of pure imaginary numbers: Any positive real number b, where i is the imaginary unit and bi is called the pure imaginary number.

it is a symbol for a specific number Definition of pure imaginary numbers: i is not a variable it is a symbol for a specific number

Simplify each expression.

Simplify each expression. Remember Remember

Simplify. To figure out where we are in the cycle divide the exponent by 4 and look at the remainder.

Divide the exponent by 4 and look at the remainder. Simplify. Divide the exponent by 4 and look at the remainder.

Definition of Complex Numbers Any number in form a+bi, where a and b are real numbers and i is imaginary unit.

When adding or subtracting complex numbers, combine like terms.

Simplify.

Simplify.

Multiplying complex numbers. To multiply complex numbers, you use the same procedure as multiplying polynomials.

Simplify. F O I L

Simplify. F O I L

Conjugates In order to simplify a fractional complex number, use a conjugate. What is a conjugate?

are said to be conjugates of each other.

Lets do an example: Rationalize using the conjugate Next

Reduce the fraction

Lets do another example Next

Try these problems.