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Complex Numbers Properties & Powers of i Operations with Complex Numbers Practice Problems

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Properties of i 2

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Powers of i 3

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Addition and Multiplication of Complex Numbers Treat as you would a variable Remember the powers of i 4

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Addition of Complex Numbers Example 5

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Multiplication of Complex Numbers Example 6

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More Examples of Operations with Complex Numbers 7

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Even More Examples of Operations with Complex Numbers 8

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And Even More Examples of Operations with Complex Numbers 9

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Quotients of Complex Numbers Solve as you would with a radical in the denominator Multiply by a quotient which simplifies to 1 and whose denominator when multiplied by the denominator of the original problem creates a real number In the case of a polynomial, multiply the conjugate (i.e. ) NEVER leave a complex number in the denominator 10

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Quotients of Complex Numbers Example 11

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Quotients of Complex Numbers Example 12

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Roots of Negative Numbers 13

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Quadratic Equation with Complex Solutions 14

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Equation with Complex Solutions 15

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Practice Problems Page 102 Problems

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