Pc9 8 powersrootsc notes
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De Moivre's Theorem allows one to find powers of complex numbers in polar form and can be used for rational values of n, including integers and fractions. The document provides examples of using De Moivre's Theorem to find powers and roots of complex numbers expressed in rectangular and polar form. Students are assigned exercises to find specific powers of complex numbers using De Moivre's Theorem and expressing the results in rectangular form.
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P cch9 sg
The document is a study guide for precalculus chapter 9. It defines key terms related to complex numbers such as absolute value, imaginary number, modulus, and polar and rectangular forms. It provides examples of converting between polar and rectangular coordinates. It also gives examples of simplifying, adding, subtracting, multiplying, dividing and taking powers of complex numbers. The student is asked to work through these examples and express answers in rectangular or polar form depending on the question.
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maths revision to help you
Here are the steps to solve this problem:
1) A is a 3×2 matrix and B is a 2×3 matrix.
2) Since the number of columns in A equals the number of rows in B, the product AB can be evaluated.
3) To find AB, multiply the elements in each row of A by the corresponding elements in each column of B and add the results:
(3 1 1)×(1 1 2)+(1 2 0)×(1 0 1)+(1 2 0)×(1 1 1)
= 3+1+0, 1+0+2, 1+0+1
= [4 2 2]
Therefore, the product AB is the
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This document contains notes from multiple days of function lessons. It includes examples of functions in standard form and their x-intercepts and y-intercepts. It also gives practice problems finding outputs of functions like f(x) = 2x - 5 for various inputs. The notes describe setting up function stations to practice notation, the vertical line test, real-world illustrations, domains and ranges. It concludes with reminders about an upcoming quiz on functions and making up any missed work.
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The document is a study guide for precalculus chapter 9. It defines key terms related to complex numbers such as absolute value, imaginary number, modulus, and polar and rectangular forms. It provides examples of converting between polar and rectangular coordinates. It also gives examples of simplifying, adding, subtracting, multiplying, dividing and taking powers of complex numbers. The student is asked to work through these examples and express answers in rectangular or polar form depending on the question.
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The document solves the trigonometry problem of cos 4θ + cos 2θ = 0 by using trigonometric identities like the double angle formula and factoring techniques. It expresses cos 4θ in terms of cos 2θ using the double angle formula, factors the resulting polynomial, and then solves each factor independently. This results in three solutions for θ: θ = π/2 + k1π, θ = π/6 + k2π, and θ = 5π/6 + k3π, where k1, k2, k3 are integers.
maths revision to help you
Here are the steps to solve this problem:
1) A is a 3×2 matrix and B is a 2×3 matrix.
2) Since the number of columns in A equals the number of rows in B, the product AB can be evaluated.
3) To find AB, multiply the elements in each row of A by the corresponding elements in each column of B and add the results:
(3 1 1)×(1 1 2)+(1 2 0)×(1 0 1)+(1 2 0)×(1 1 1)
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= [4 2 2]
Therefore, the product AB is the
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This document contains notes from multiple days of function lessons. It includes examples of functions in standard form and their x-intercepts and y-intercepts. It also gives practice problems finding outputs of functions like f(x) = 2x - 5 for various inputs. The notes describe setting up function stations to practice notation, the vertical line test, real-world illustrations, domains and ranges. It concludes with reminders about an upcoming quiz on functions and making up any missed work.
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- 2. Classwork (turn in on a separate sheet of paper): Find each power. Express the result in rectangular form. 3 π π 1. 3 cos 6 + ι σ 6 ιν 4 2. (1 + 3ι) −2 3. ( 2 + 3ι) 4. 4 2 + 6ι