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