1.3 complex number system. complex numbers numbers of the form a + bi, where a and b are real...

1.3 Complex Number System

Complex NumbersNumbers of the form a + bi,

where a and b are real numbers and i is the imaginary

unit.

Add / Subtract Complex Numbers

1. Change (– ) to (+) of the opposite

2. 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 other polynomials

3. Follow your 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.

Simplify using Conjugates

Dividing Complex Numbers

1. You cannot have an i in the denominator

2. Multiply numerator and denominator by the conjugate of the denominator

3. FOIL Method for multiplying binomials

4. Follow your rules of exponents5. Combine all like terms6. Write your answer in the form of

a + bi

Simplify each expression in standard form

Evaluate Powers of i

Evaluate Square Roots

Perform the indicated operation and express your answer in

standard form

Perform the indicated operation and express your answer in

standard form

Character of Solutions

Determine the character of the solutions of each quadratic

equation.

Solve each equation in the complex number system