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7.3 Complex Numbers: Trig Form Day 1

7.3 Complex Numbers: Trig Form Day 1. Do Now Simplify (2 + i ) (3 – 2i) i^33. HW Review: p.198 #1-85. Graphing Complex Numbers. Complex numbers can be graphed just like real numbers The horizontal (x) axis is the real axis The vertical (y) axis is the imaginary axis. Ex.

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7.3 Complex Numbers: Trig Form Day 1

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  1. 7.3 Complex Numbers: Trig FormDay 1 Do Now Simplify (2 + i) (3 – 2i) i^33

  2. HW Review: p.198 #1-85

  3. Graphing Complex Numbers • Complex numbers can be graphed just like real numbers • The horizontal (x) axis is the real axis • The vertical (y) axis is the imaginary axis

  4. Ex • Graph each of the following • 1) 3 + 2i • 2) -4 – 5i • 3) -3i

  5. Absolute Value of a Complex Number • The absolute value of a complex number a + bi is

  6. Ex • Find the absolute value of each • 1) 3 + 4i • 2) -2 – i • 3) 4/5 i

  7. Trigonometric Notation for Complex Numbers • Let’s consider the angle created by a complex number a + bi • This is trigonometric notation for a complex number

  8. Trig Notation for Complex Numbers • r is the absolute value of a + bi • Theta is called the argument of a + bi • This notation is also known as polar notation

  9. Ex • Find trigonometric notation for each of the following • 1) • 2)

  10. Ex • Find standard notation, a + bi, for each of the following complex numbers • 1) • 2)

  11. Closure • Write -5 + 5i in trigonometric notation • HW: p.632 #1-31 odds • 7.1-7.3 Quiz Thurs April 24

  12. Complex Numbers: Trig FormDay 2 • Do Now • Find trigonometric notation for 2 + 3i

  13. HW Review: p.632 #1-31 odds

  14. Complex Numbers: Multiplication • For any complex numbers

  15. Ex • Multiply

  16. Ex • Multiply

  17. Ex • Convert to trigonometric notation and multiply

  18. Complex Numbers: Division • For any complex numbers

  19. Ex • Divide

  20. Ex • Convert to trigonometric notation and divide

  21. Closure • Multiply • HW: p.632 #33-43 odds

  22. Complex Numbers: Trig FormDay 3 • Do Now • Convert to trig notation

  23. HW Review: p.632 #33-43

  24. DeMoivre’s Theorem • For any complex number and any natural number n,

  25. Ex • Find each of the following • 1) • 2)

  26. Roots of Complex Numbers • The nth roots of a complex number are given by • Where k = 0, 1, 2, …, n-1

  27. Ex • Find the square roots of

  28. Ex • Find the cube roots of 1

  29. Closure • Evaluate in trigonometric notation • HW: p.633 #45-75 odds

  30. 7.1-7.3 ReviewDay 4 • Do Now • Find all complex solutions of the equation

  31. HW Review: p.633 #45-75

  32. 7.1-7.3 Review • 7.1 Law of Sines • Solve triangles • Find area of triangles • 7.2 Law of Cosines • Solve triangles • 7.3 Complex Numbers in Trig Notation • Trig notation of complex numbers • Multiply, divide, powers, and roots

  33. Closure • When do we use the Law of Sines versus the Law of Cosines to solve triangles? • What is trigonometric notation for complex numbers • 7.1-7.3 Quiz Tomorrow

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