Lesson 13

Lesson 13 - Lesson 13 Example 1: Solve the following...

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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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