Pc sections p.6-p.7
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Transcript of Pc sections p.6-p.7
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COMPLEX NUMBERSSection P.6
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i
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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.
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Properties
Commutative properties of addition and multiplication
Associative properties of addition and multiplication
Distributive properties of multiplication over addition and subtraction.
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Properties
Additive identity is 0 or
Additive inverse of is , because
Multiplicative identity is or
Multiplicative inverse or reciprocal of a+bi is
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Multiplying Complex Numbers
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Dividing Complex Numbers
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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.
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SOLVING INEQUALITIESSection P.7
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Absolute Value Inequalities
If , then u is in the interval
If , then u is in the interval or or
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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.
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Other Inequalities
𝑥3 – 𝑥 2– 30 𝑥≤0
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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.?
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Classwork
Page 53 #33-43 odd Page 58 #1-5 odd, 9-15 odd, 33, 34