5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property....
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Transcript of 5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property....
![Page 1: 5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify.…](https://reader038.fdocuments.us/reader038/viewer/2022101123/5a4d1be97f8b9ab0599e38ae/html5/thumbnails/1.jpg)
5.9 Complex NumbersAlg 2
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![Page 3: 5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify.…](https://reader038.fdocuments.us/reader038/viewer/2022101123/5a4d1be97f8b9ab0599e38ae/html5/thumbnails/3.jpg)
Express the number in terms of i.
Factor out –1.
Product Property.
Simplify.
Multiply.
Express in terms of i.
![Page 4: 5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify.…](https://reader038.fdocuments.us/reader038/viewer/2022101123/5a4d1be97f8b9ab0599e38ae/html5/thumbnails/4.jpg)
Express the number in terms of i.
Factor out –1.
Product Property.
Simplify.
Express in terms of i.4 6 4 6i i
![Page 5: 5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify.…](https://reader038.fdocuments.us/reader038/viewer/2022101123/5a4d1be97f8b9ab0599e38ae/html5/thumbnails/5.jpg)
Express the number in terms of i.
![Page 6: 5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify.…](https://reader038.fdocuments.us/reader038/viewer/2022101123/5a4d1be97f8b9ab0599e38ae/html5/thumbnails/6.jpg)
Answer: = 6
Simplify .
![Page 7: 5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify.…](https://reader038.fdocuments.us/reader038/viewer/2022101123/5a4d1be97f8b9ab0599e38ae/html5/thumbnails/7.jpg)
Simplify
Multiplying powers
Power of a Power
Answer:
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Solve the equation.
Take square roots.
Express in terms of i.
Checkx2 = –144
–144–144–144
(12i)2
144i 2
144(–1)
x2 = –144–144–144–144144(–1)
144i 2
(–12i)2
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x2 + 48 = 0
Solve the equation.
Add –48 to both sides.
Take square roots.
Express in terms of i.
x2 = –48
Check x2 + 48 = 0000
(48)i 2 + 48
+ 48
48(–1) + 48
![Page 10: 5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify.…](https://reader038.fdocuments.us/reader038/viewer/2022101123/5a4d1be97f8b9ab0599e38ae/html5/thumbnails/10.jpg)
Every complex number has a real part a and an imaginary part b.
A complex number is written in the form a + bi, where a and b are real numbers and i = .
Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.
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Find the values of x and y that make the equation 4x + 10i = 2 – (4y)i true .
Equate the real parts.
4x + 10i = 2 – (4y)i
Real parts
Imaginary parts
4x = 2
Solve for y.Solve for x.
Equate the imaginary parts.
10 = –4y
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Find the values of x and y that make each equation true.
Equate the real parts.
Real parts
Imaginary parts
–8 = 5x
Solve for y.Solve for x.
Equate the imaginary parts.
–8 + (6y)i = 5x – i 6
–8 + (6y)i = 5x – i 6
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The solutions and are related. These solutions are a complex conjugate pair. Their real parts are equal and their imaginary parts are opposites.
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andare conjugates.
Multiply.
Answer: Standard form
Simplify .