What is the justification for step B?
Review the proof of de Moivre’s theorem.
Proof of de Moivre's Theorem
[cos(θ) + i sin(θ)]k + 1
A = [cos(θ) + i sin(θ)]k ∙ [cos(θ) + i sin(θ)]1
B = [cos(kθ) + i sin(kθ)] ∙ [cos(θ) + i sin(θ)]
C = cos(kθ)cos(θ) − sin(kθ)sin(θ) + i [sin(kθ)cos(θ) + cos(kθ) sin(θ)]
D = cos(kθ + θ) + i sin(kθ + θ)
E = cos[(k + 1)θ] + i sin[(k + 1)θ]
A) distributive property
B) factoring
C) multiplication rule
D) assumption (for n = k step)
