Review the proof of de Moivre's theorem. What is the justification for step B?
Proof of de Moivre's Theorem
O distributive property
O factoring
O multiplication rule
O assumption (for n= k step)
[cos(O) + i sin(e)]+1
A = (cos(0) + i sin(O)]* . [cos(O) + i sin(O)]
B = [cos(ko) + i sin(ke)] . [cos(0) + i sin(O)]
C = cos(KO)cos(0) - sin(ko)sin(0) +i (sin(ko) cos(0) +
cos(ko) sin(0)]
D = cos(kO + ) + i sin(ke + 0)
E = cos[(k + 1)] + i sin[(k + 1)]