Homework Quiz 1. List all possible rational zeros for the function f(x)=x 3 -4x 2 -4x+16 2. Find all real solutions of the polynomial equation. Solve algebraically.

Homework Quiz1. List all possible rational zeros for the

function f(x)=x3-4x2-4x+16

2. Find all real solutions of the polynomial equation . Solve algebraically but check graphically.

x4 – x3 -29x2 –x -30 =0

Imaginary Numbersi2 = - 1

i = √-1

Complex NumbersMade up of adding real numbers to multiples

of imaginary numbers

bia

Adding and Subtracting Complex Numbers 1. )32()3( ii

PropertiesMany of the properties of real numbers are

valid for complex numbers as well includingAssociative Property of Addition and

MultiplicationCommutative Property of Addition and

MultiplicationDistributive Property of Multiplication

Multiplying Complex Numbers1. )34)(2( ii

ConjugatesNotice in the previous slide the product of

was a real number.

This happens when you multiply a complex number by its conjugate

)23)(23( ii

ExampleMultiply 3 – 5i by its conjugate

Quotient of Complex NumbersWrite in standard form

i

i

24

32

Plotting Complex Numbers

HomeworkP. 133 #5, 9, 15-51 every other odd, 67-72 on

same plane