a2t review of complex numbers/ properties of quadratic ......algebra2/trig test 5-packet #2: complex...
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A2T
Review of
Complex Numbers/
Properties of
Quadratic Equations
Algebra2/Trig Test 5-Packet #2: Complex
Numbers/Properties of Quadratic equations
COMPLEX NUMBERS
Definition of Simplifying negative radicals
Powers of (pure imaginary numbers)
Graphing Complex numbers
Operations Complex Numbers
Additive inverse, multiplicative inverse, (including rationalizing) QUADRATICS
Solving a Quadratic Equation with complex roots o By completing the square o By the quadratic formula
The Nature of the Roots: The Discriminant
The Sum and Product of the Roots of a Quadratic
Solving Higher Degree Polynomial equations
Concept 1: Definition of i / Simplifying negative radicals/ Powers of
1.
2.
3.
4.
5.
Concept 2: Graphing Complex numbers
6.
7.
8.
9.
10. Two Complex numbers are graphed below. What is the sum expressed in standard complex number form?
1 2 3 4 5 6 7 8–1–2–3–4–5–6–7–8 real
1
2
3
4
5
6
7
8
–1
–2
–3
–4
–5
–6
–7
–8
imag.
Concept 3: Operations Complex Numbers
11. Simplify.
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Concept 4: Additive inverse, multiplicative inverse, (including rationalizing)
16.
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20. Divide.
21. Divide.
Concept 5: Solving Quadratic Equations with complex roots
22. 23.
24. 25.
Solve the equation by using the quadratic formula. 26.
27.
28.
Concept 6: The Nature of the Roots: The Discriminant
29. If a quadratic equation has 2 roots, how many times will its graph cross the x-axis?
________
30. If a quadratic equation has 1 root, how many times will its graph cross the x-axis?
________
31. If a quadratic equation has no roots, how many times will its graph cross the x-axis?
________
32. What is the value of the discriminant of the quadratic function below?
a) Less than zero
b) Equal to zero
c) Greater than zero
d) Perfect Square Number
33. If a problem says that the roots are….
o real, set the discriminant ________ and solve
o imaginary, set the discriminant ________ and solve
o equal, set the discriminant ________ and solve.
34.
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39.
Concept 7: The Sum and Product of the Roots of a Quadratic
40. If a quadratic has one root that’s , what MUST the other root be? __________
Explain. ____________________________________________________________________________
41. If a quadratic has one root that’s √ , what MUST the other root be? __________
Explain. ____________________________________________________________________________
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50.
Concept 8: Solving Higher Degree Polynomial equations
51.
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53. Find all roots.
54.
55.
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