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Complex Numbers. Lesson 5.1. It's any number you can imagine. The Imaginary Number i. By definition Consider powers if i. Using i. Now we can handle quantities that occasionally show up in mathematical solutions What about. Imaginary part. Real part. Complex Numbers.

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Presentation Transcript
Complex numbers

Complex Numbers

Lesson 5.1


The imaginary number i

It's any number you can imagine

The Imaginary Number i

  • By definition

  • Consider powers if i


Using i
Using i

  • Now we can handle quantities that occasionally show up in mathematical solutions

  • What about


Complex numbers1

Imaginary part

Real part

Complex Numbers

  • Combine real numbers with imaginary numbers

    • a + bi

  • Examples


Try it out
Try It Out

  • Write these complex numbers in standard form a + bi


Operations on complex numbers
Operations on Complex Numbers

  • Complex numbers can be combined with

    • addition

    • subtraction

    • multiplication

    • division

  • Consider


Operations on complex numbers1
Operations on Complex Numbers

  • Division technique

    • Multiply numerator and denominator by the conjugate of the denominator


Complex numbers on the calculator
Complex Numbers on the Calculator

  • Possible result

  • Reset modeComplex formatto Rectangular

  • Now calculator does desired result


Complex numbers on the calculator1
Complex Numbers on the Calculator

  • Operations with complex on calculator

Make sure to use the correct character for i. Use 2nd-i


Warning
Warning

  • Consider

  • It is tempting to combine them

    • The multiplicative property of radicals only works for positive values under the radical sign

    • Instead use imaginary numbers


Try it out1
Try It Out

  • Use the correct principles to simplify the following:


Assignment
Assignment

  • Lesson 5.1

  • Page 340

  • Exercises 1 – 69 EOO


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