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MTH 095 Intermediate Algebra Chapter 10 Complex Numbers and Quadratic Equations Section 10.1 Complex Numbers Copyright © 2011 by Ron Wallace, all rights reserved.

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Review: Simplifying Square Roots of Positive Numbers a.Roots of “perfect” squares –Result is an integer b.Roots of multiples of perfect squares –Result is an integer multiple of a square root (i.e. simplified) c.Roots of all other positive numbers –Result is the square root (i.e. can’t be simplified)

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Square Roots of Negatives Since the square of any number is positive, then you might concluded that the square root of a negative number is not “real” … but … Definition: Therefore … That is, in a sense, –1 is a perfect square.

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Square Roots of Negatives So … since … for b > 0 …

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Imaginary Numbers The set of numbers of the form … –That is, the product of a real number and i.

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Imaginary Numbers Operations … –Addition –Subtraction –Multiplication –Division

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Complex Numbers Real Numbers Imaginary Numbers What happens when you take a real number and an imaginary number and … Multiply? Divide? Add? Subtract?

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Complex Numbers Real Numbers Imaginary Numbers Imaginary partReal part Complex Numbers

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Complex Numbers Operations … –Addition

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Complex Numbers Operations … –Subtraction

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Complex Numbers Operations … –Multiplication

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Complex Numbers Operations … –Division

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Complex Numbers More examples with division …

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