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Warm Up

Solve Dana's rate of speed walking home from school after considering her walking time and apply properties of imaginary numbers.

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Warm Up

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  1. Warm Up Simplify Solve SAT Review question Dana walks from home to school at a rate of 5 mph. It takes her 2 hours longer to walk home from school than it did to walk to school. If her total walking time to and from school was 8 hours, what was Dana’s rate of speed walking home from school? a) 3 b) 4 c) 5 d) 8 e) 15

  2. Section 5.4 Complex Numbers Essential Question • What is an imaginary number?

  3. Imaginary Unit • Until now, you have always been told that you can’t take the square root of a negative number. If you use imaginary units, you can! • The imaginary unit is i. • i= • It is used to write the square root of a negative number.

  4. Property of the square root of negative numbers • If r is a positive real number, then Examples:

  5. *For larger exponents, divide the exponent by 4, then use the remainder as your exponent instead. Example:

  6. Examples

  7. Complex Numbers • A complex number has a real part & an imaginary part. • Standard form is: Real part Imaginary part Example: 5+4i

  8. Adding and Subtracting complex numbers1. add or subtract the real parts2. add or subtract the imaginary parts Ex: Ex:

  9. You try!

  10. Multiplying1. Treat the i’s like a variable2. Change any that are not to the first power Ex: Ex:

  11. You try!

  12. Conjugates • The conjugate of a complex number has the same real part and the opposite imaginary part • Ex. Find the conjugate of 5 + 3i 5 – 3i Ex. Find the conjugate of 3 – 2i 3 + 2i

  13. Imaginary numbers in the denominator • i’s cannot be in the denominator (like radicals) • To get rid of the i’s, multiply numerator and denominator by the conjugate • If there is only an imaginary part in the denominator, multiply by the same imaginary number

  14. Example

  15. You try!

  16. AssignmentPg. 277: #17-21(odd), 29-33(odd), 37-41(odd), 47-51(odd), 57-61(odd), 65-69(odd), 92

  17. Assessment • Concept circles

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