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Alg2 2.5 Notes.notebook
1
September 29, 2014
warmup
6.7.
Solve.
Simplify each expression.
25 Complex Numbers and Roots
Warmup ans.
Alg2 2.5 Notes.notebook
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September 29, 2014
Learning Target
25 Complex Numbers and Roots
Define and use imaginary and complex numbers.
Solve quadratic equations with complex roots.
To find all the roots in a polynomial.To transform problems into a much simpler problem.To model how electrical circuits or forced spring/damper
systems behave.To keep track of amplitude and phase of an electrical
oscillation, such as an audio signal, or the electrical voltage and current that power electrical appliances.
To make pretty pictures.
De Moivre's theorem
Mandelbrot Set
Mandelbrot Set
The Mandelbrot set is a mathematical formula which uses the complex plane to make stunning pictures. Here is a picture of one part of the Mandelbrot set.
Alg2 2.5 Notes.notebook
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Definitions
I. Defining Imaginary Numbersvs.
vs.
Simplifying square roots
II. Simplifying Square Roots
Alg2 2.5 Notes.notebook
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September 29, 2014
You try
2)1) 3)
Solving Quadratic Eq.
III. Solving Quadratic Equations4) x2 + 144 = 0 Let's check:
Alg2 2.5 Notes.notebook
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September 29, 2014
Equating Complex Numbers
IV. Defining and Equating Two Complex Numbers
a + biComplex Form
iff
6) Find x and y:
Finding Complex Zeros
V. Finding Complex Zeros of Quadratic Functions
7) Find the zeros of the function by completing the square.f(x) = x2 + 10x + 26
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Finding Complex Conjugates
VI. Finding Complex ConjugatesThe complex conjugate of any complex number
a + bi is the complex number a – bi.
Examples:
Why is this important?When given one complex root, you can always find the other by finding its conjugate.
8 + 5i
Warning!
Alg2 2.5 Notes.notebook
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September 29, 2014
You try
Now you try ans.
Alg2 2.5 Notes.notebook
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September 29, 2014
Homework
2.5 p.97 #3 33 (x3), 38, 40, 44, 5866 all, 7680
