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    Complex Variables : Complex Variables : De Moivre's Theorem and Rectangular Coordinates Theorem and Rectangular Coordinates

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    5. Use de Moivre's formula to derive the following trigonometric identities.
    (a) cos 3θ = cos3 θ - 3cos θּsin2 θ
    (b) sin 3θ = 3cos2 θּsin θ - sin3 θ

    6. By writing the individual factors on the left in exponential form, performing the needed operations, and finally changing back to rectangular coordinates, show that

    (a) i (1 - sqrt (3)ּi) (sqrt (3) + i) = 2 (1+ sqrt (3)ּi)
    (b) 5i / (2 + i) = 1 + 2i
    (c) (-1 + i)7 = -8 (1 + i)
    (d) (1 + sqrt (3)ּi)-10 = 2-11(-1 + sqrt (3)ּi)

    *sqrt means square root.

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    © BrainMass Inc. brainmass.com March 4, 2021, 6:10 pm ad1c9bdddf
    https://brainmass.com/math/complex-analysis/de-moivre-theorem-rectangular-coordinates-theorem-32497

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    De Moivre's Theorem and rectangular coordinates are investigated. The solution is detailed and well presented.

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