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6.7 The Imaginary Number i
Rational Number: any number that can be written as a quotient of integers. This includes repeating decimals:
, ,
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Irrational Number: a number with a decimal that does not repeat and does
not end: ,
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Real Number: the set of rational and irrational numbers•
Imaginary Number: the letter i that is used to represent
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Pure Imaginary Number: any number written in the form where b is a
non-zero real number:
,
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So …
, therefore
And …
If r is a positive real number, then
Examples:
Simplify
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Combine
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Multiply
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11.19.12Tuesday, July 17, 201210:31 PM
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Notice: the rule
does NOT apply if a and b are both negative. You must FIRST express the radicals as pure imaginary numbers before combining.
Examples:
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Solve •
Practice:
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Homework: MathXL 6.7
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