Sets of Real and Complex Numbers



Sets of Real and Complex Numbers

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A complex number is of the form a+bi, where a and b are real numbers.

The ___________ of a complex number a+bi is a-bi

The numbers 5+7i and 5-7i are __________________

What is the conjugate of 8i ?

Adding, Subtracting, and Multiplying Complex Number Examples:

Examples - Dividing

Multiply by the conjugate of the denominator.

Make sure in a+bi form in the end.

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The powers of i cycle through the values i, -1, -i, 1.

i = i5 =

i2 = i6 =

i3 = i7 =

i4 = i8 =

i0 =

Example - Simplify

i37 = i58 =

i75 = i80 =

(-i)75 = (2i)80 =

Operations Review

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Examples:

Suppose that $1250 is invested at 4.6%

interest, compounded quarterly. How

much is in the account at the end of

8 years?

Rational Expressions

Simplifying Rational Expressions

Multiplying and Dividing Rational Expressions

Multiply across the top and across the bottom. Then simplify as much as you can.

Divide by flipping the second fraction.

Adding and Subtracting Rational Expressions

Need same denominators to add or subtract.

If they are not the same find least common denominator.

You may need to factor first to find it.

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Radical Notation and Rational Exponents

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Relations and Functions

A relation is a set of pairs of input and output values.

Every input has at least one output.

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Find the domain of each.

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Using Functions

Sum, Difference, Product, Quotient of functions

Composition of Functions Decomposing a Function

If h(x) = (2x - 3)5, find f(x) and g(x) such that h(x) = (f○g)(x).

Simple Inverse Functions

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3 Nifty Things About Inverses

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If a function is one-to-one, its inverse is a function

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