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Name:__________ warm-up 4-4 Solve x 2 – x = 2 by factoringSolve c 2 – 16c + 64 = 0 by factoring Write a quadratic equation with the roots –1 and 6 in the form ax 2 + bx + c, where a, b, and c are integers.

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Solve 2x 2 + 5x + 3 = 0 by factoring In a rectangle, the length is three inches greater than the width. The area of the rectangle is 108 square inches. Find the width of the rectangle.

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Details of the Day EQ: How do quadratic relations model real-world problems and their solutions? Depending on the situation, why is one method for solving a quadratic equation more beneficial than another? How do transformations help you to graph all functions? Why do we need another number set? I will be able to… Activities: Warm-up Collect Lab Project Review homework Notes: 4-4 Complex Numbers Class work/ HW Vocabulary: imaginary unit pure imaginary number complex number complex conjugates. Perform operations with pure imaginary numbers. Perform operations with complex numbers.

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A Quick Review Solve x 2 – x = 2 by factoringSolve c 2 – 16c + 64 = 0 by factoring Write a quadratic equation with the roots –1 and 6 in the form ax 2 + bx + c, where a, b, and c are integers.

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A Quick Review Solve 2x 2 + 5x + 3 = 0 by factoring In a rectangle, the length is three inches greater than the width. The area of the rectangle is 108 square inches. Find the width of the rectangle.

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Notes and examples i

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Simplify –3i 2i. Simplify 3i 5i

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Notes and examples Simplify:Solve: 5y 2 + 20 = 0 Original equation Subtract 20 from each side. Divide each side by 5 Take the square root of each side Solve 2x 2 + 50 = 0

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Notes and examples Find the values of x and y that make the equation 2x + yi = –14 – 3i true. Set the real parts equal to each other and the imaginary parts equal to each other. Real partsImaginary parts

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Notes and examples Find the values of x and y that make the equation 3x – yi = 15 + 2i true Simplify (3 + 5i) + (2 – 4i). Simplify (4 – 6i) – (3 – 7i).Simplify (2 + 6i) + (3 + 4i

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Notes and examples Simplify (3 + 2i) – (–2 + 5i). ELECTRICITY In an AC circuit, the voltage E, current I, and impedance Z are related by the formula E = I Z. Find the voltage in a circuit with current 1 + 4j amps and impedance 3 – 6j ohms.

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Notes and examples

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Introduction Completing the square can be a long process, and not all quadratic expressions can be factored. Rather than completing the square or factoring,

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