**Unformatted text preview: **Lesson 13
Example 1: Solve the following quadratic equations
a.
b.
Does have any real solutions? Why or why not? Does have any solutions? Complex Number:
, where and are real numbers and
is the real part and is the imaginary part
Review of the Product Rule for Exponents:
a. b. Review of the Power Rule for Exponents:
a. ( ) b. ( ) √ Example 2: Write each expression in the form
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
Do you notice a pattern?
Example 3: Write each expression in the form
a. b. c. d. Example 4: Write each expression in the form
)(
)
a. ( b. ( )( c. ( ) ) Solving equations containing complex numbers:
- group the real parts with the real parts and the imaginary parts with
the imaginary parts Example 5: For each of the following equations, identify the real parts
and the imaginary parts. Then find the values of and
)
a. ( b. ( ) Conjugate:
- writing the same two terms with the opposite operation (addition
changes to subtraction or vice versa)
Complex conjugate:
- writing a complex number with the same real and imaginary parts,
but with the opposite operation
Quotients of complex numbers:
- multiply the expression by ( ) - this can thought of as rationalizing the denominator (eliminate the
imaginary numbers from the denominator)
Example 6: Write each expression in the form
a. b. c. Example 7: Write each expression in the form
a. (
)(
)
√
√ √ b. c. √ √
√ √ Example 8: Solve the following equations; if your answer is a complex
number, express in the form
a. b. c. ...

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