pc sections p.6-p.7
TRANSCRIPT
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