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WARM UP Is x-2 a factor of x 2 - x -2. verify using synthetic division or long division.

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MATH IV LESSON10 COMPLEX NUMBERS 2.4 Essential Question: How do you perform operations with complex numbers? Standard: MM4A4. Students will investigate functions. a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

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Complex number: a number composed of a real part and an imaginary part. Standard form of a complex number: a + bi Pure imaginary number: bi Equality of complex numbers: if a + bi = c + di, then a = c and b = d Imaginary unit i: the square root of negative one.

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A complex number has both an imaginary part and a real part, and is written in standard form a + bi

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If a + bi = c + di, then a = c, and b = d Example problem: a + bi = i Solve for a and b

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Example: (3-i) + (2 + 3i) (3-i) + (2 + 3i) = 5 + 2i Combine like terms Example: (3 – i) – (2 + 3i) Distribute your negative sign to get 3 – i – 2 – 3i Then combine like terms to get 1 - 4i

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MULTIPLYING COMPLEX NUMBERS

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(2-i)(4 + 3i) =

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If a complex number has the form a + bi Then its complex conjugate is a – bi Example: Find the complex conjugate of 6 – 7i

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(3-5i)(3+5i) = Multiplying complex conjugates

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Graph: 3 + 5i 2 + 3i And 1 -2i Real axis Imaginary axis

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P 138 # 1, 5, odd, 25,29,37,38, 65,66

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