Complex Number System

• Adding, Subtracting, Multiplying and Dividing Complex Numbers

• Simplify powers of i

Complex NumbersNumbers of the form a + bi,

where a and b are real numbers and i is the

imaginary unit.

Adding and Subtracting

Complex Numbers1. Change (-) to (+) of the

opposite2. Apply the Distributive Property3. Combine all like terms4. 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 exponents4. Combine all like terms5. 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 exponents5. Combine all like terms6. Write your answer in the form of

a + bi

Simplify each expression in standard form

Evaluating Powers of i

11 9 5 37. 12i 7i 4i 6i 15 13 10 78. 4i 7i 8i 2i

Evaluating Square Roots

Perform the indicated operation and express your

answer in standard form

Perform the indicated operation and express your

answer in standard form