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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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Principal Square Root – square root of b, denoted , for b > 0, is the positive number a such that a2 = b.

Examples:

Simplify.

For any root n and any nonnegative numbers a and b,

Examples:

Simplify

For any root n and any nonnegative numbers a and b, b≠0,

Examples:
Simplify

Homework: pg. 528 #9,13,17,21,23,25,27,29,33,43,45,47,49,51,53,55,57,59,67,71

Rational Exponents

Recall:

For any integer n > 1, we define to be the nth root of a, or

Examples:
Simplify.

For any integers m and n, n > 1, we define to be

Examples:
Simplify.

Examples:
Simplify.

Homework: pg. 575 #3,9,11,13,15,17,19,33,35,37,39,43,45,53,55,63,65

Simplify.

Examples:

Homework: pg. 582 #3,5,7,9,11,13,15,17,19,25,29,35,39,49,55,57,59,61

Multiplication and Division of Radical Expression

Examples:
Multiply.

Rationalizing the Denominator:
Examples:
Rationalize the denominator.

Homework: pg. 592 #5,7,13,15,19,23,25,27,33,35,37,39,41,45,47,49,55,61,65,67,75

Examples:
Solve.

6. For find all values for x for which f(x) = 9.

Homework: pg. 603 #7,9,11,13,17,19,21,25,27,29,31,33,39

Complex Numbers

Examples:

1. Express in terms of i.

2. Express in terms of i.

3. Express − in terms of i.

Complex Number: a + bi, where a is the real part and bi is the imaginary part.

Examples:
1. Simplify:

a. (3 + 12i) + (-8 + 15i)

b. (14 – 6i) – (3 + 22i)

2. Multiply.

a. (4i)(15i)

c. -6i(7 + 8i)

d. (3 – 2i)(8 + i)

e. (9 – 4i)2

f. (7 + 4i)(7 – 4i)

Examples:
Divide.

Powers of i:

Homework: pg. 613 #7,9,13,19,23,25,33,35,45,47,51,53,651,63,65,69,71,73