Complex Number System Adding, Subtracting, Multiplying and Dividing Complex Numbers Simplify powers of i

Complex Numbers Numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit.

Adding and Subtracting Complex Numbers 1.Change (-) to (+) of the opposite 2.Apply the Distributive Property 3.Combine all like terms 4.Write your answer in the form of a + bi

Simplify each expression in standard form

Multiplying Complex Numbers 1.FOIL Method for multiplying binomials 2.Distributive Property for all others 3.Follow the rules of exponents 4.Combine all like terms 5.Write your answer in the form of a + bi

Simplify each expression in standard form

Conjugate

The conjugate of the conjugate of a complex number is the complex number itself. The conjugate of the sum of two complex numbers equals the sum of their conjugates. The conjugate of the product of two complex numbers equals the product of their conjugates.

Simplifying w/Conjugates

Dividing Complex Numbers 1.You cannot have an i in the denominator 2.Multiply by conjugate of denominator 3.FOIL Method for multiplying binomials 4.Follow the rules of exponents 5.Combine all like terms 6.Write your answer in the form of a + bi

Simplify each expression in standard form

Evaluating Powers of i

Evaluating Square Roots Perform the indicated operation and express your answer in standard form