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Imaginary numbers and DeMoivre’s theorem

Imaginary numbers and DeMoivre’s theorem. Dual 8.3. Remember Complex Numbers: a + b i a = real number b = imaginary number . Plot the following points. 3 + 4i 2 – i 4i -3. Converting Rectangular to Polar Form . Polar form of a Complex number:. x = r cos ( θ )

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Imaginary numbers and DeMoivre’s theorem

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  1. Imaginary numbers andDeMoivre’s theorem Dual 8.3

  2. Remember Complex Numbers: a + b ia = real number b = imaginary number Plot the following points. 3 + 4i 2 – i 4i -3

  3. Converting Rectangular to Polar Form Polar form of a Complex number: x = r cos (θ) y = r sin (θ) a + b i a+bi b (or y) a (or x) Rem: if x neg add 180 If y only neg. add 360

  4. Example:

  5. Converting Polar to Rectangular Form x = r cos (θ) y = r sin (θ) Example:

  6. Operations with Complex Numbers: All these can be worked much easier in POLAR FORM.

  7. MULTIPLICATION Multiplying in Polar form

  8. DIVISION

  9. POWERS AND ROOTS Formula:

  10. INDIVIDUAL ROOT

  11. ALL ROOTS Add 360 3 solutions 1 real and 2 imaginary Change to complex Add 360 Conjugate pairs

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