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Complex Numbers

# Complex Numbers - Chp.5.4ComplexNumbers February28,2013...

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Chp. 5.4 ­ Complex Numbers Algebra II 1 February 28, 2013 Date: Chapter: Chapter 5:4 ­­> Complex Numbers Objectives: Perform operations with pure imaginary numbers and complex numbers

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Chp. 5.4 ­ Complex Numbers Algebra II 2 February 28, 2013 Notes: Consider the graph of y = x 2 + 2x + 4. Notice how this graph has no x­intercepts and therefore does not have any roots. Does this mean there are no solutions? * Imaginary Unit (i) = Principal √­1 therefore i = √­1 * Pure Imaginary Numbers = Square root of negative real numbers; for any positive real number b, √­b 2 = √b 2 times √­1 = bi ­­­The Commutative and Associative Properties of Multiplication hold true for pure imaginary numbers­­­ * Complex Numbers = An expression that contains both a real number and an imaginary number. (a ± bi) where a = real number and bi is the imaginary number * Complex Conjugates = Two complex numbers of the form a + bi and a ­ bi; the product of two conjugates is always a real number. Square Root Property ­­Method used to solve a quadratic equation­­ If x

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Complex Numbers - Chp.5.4ComplexNumbers February28,2013...

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