Complex Numbers 33 22 11 Properties & Powers of i Operations with Complex Numbers Practice...

Complex Numbers

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1 Properties & Powers of i

Operations with Complex Numbers

Practice Problems

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Properties of i

1i

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Powers of i

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1

4

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1

i

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i

ii

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Addition and Multiplication of Complex Numbers

Treat as you would a variable Remember the powers of i

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Addition of Complex Numbers Example

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Multiplication of Complex Numbers Example

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More Examples of Operations with Complex Numbers

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Even More Examples of Operations with Complex Numbers

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And Even More Examples of Operations with Complex Numbers

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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

iixx 66,33

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Quotients of Complex Numbers Example

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Quotients of Complex Numbers Example

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Roots of Negative Numbers

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Quadratic Equation with Complex Solutions

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Equation with Complex Solutions

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Practice Problems

Page 102Problems 1-34