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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
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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
