COMPLEX NUMBERSSection P.6

i

Complex Number

Any number that can be written in the form where a and b are real numbers.

The real number a is the real number part.

The real number b is the imaginary part.

, is the standard form.

Properties

Commutative properties of addition and multiplication

Associative properties of addition and multiplication

Distributive properties of multiplication over addition and subtraction.

Properties

Additive identity is 0 or

Additive inverse of is , because

Multiplicative identity is or

Multiplicative inverse or reciprocal of a+bi is

Multiplying Complex Numbers

Dividing Complex Numbers

Discriminant of a Quadratic

Given where a, b, and c are real numbers and

If , there are two distant real solutionsIf , there is one repeated real solution.If , there are two complex conjugate pair of solutions.

SOLVING INEQUALITIESSection P.7

Absolute Value Inequalities

If , then u is in the interval

If , then u is in the interval or or

Quadratic Inequalities

Always set your inequality to zero. Find the critical points, where it equal

zero. Choose numbers or use a graphing

calculator to find the solution to the inequality.

Other Inequalities

𝑥3 – 𝑥 2– 30 𝑥≤0

Projectile Motion

A projectile is launched straight up from ground level with an initial velocity of 288 ft./sec.a. When will the projectile’s height above

ground be 1152 ft.?b. When will the projectile’s height above

ground be at least 1152 ft.?

Classwork

Page 53 #33-43 odd Page 58 #1-5 odd, 9-15 odd, 33, 34