De Moivre's Theorem
(1) If n is any rational number, then (cos θ + i sin θ)n = cos nθ + i sin nθ.
(2) If z = (cos θ1 + i sin θ1) (cos θ2 + i sin θ2) (cos θ3 + i sin θ3)………… (cos θn + i sin θn)
then z = cos (θ1 + θ2 + θ3 + ……… + θn) + i sin (θ1 + θ2 + θ3 + ……… + θn)
where θ1 + θ2 + θ3 + ……… + θn ∈ R.
(3) If z = r(cos θ + i sin θ) and n is a positive integer, then
(2) If z = (cos θ1 + i sin θ1) (cos θ2 + i sin θ2) (cos θ3 + i sin θ3)………… (cos θn + i sin θn)
then z = cos (θ1 + θ2 + θ3 + ……… + θn) + i sin (θ1 + θ2 + θ3 + ……… + θn)
where θ1 + θ2 + θ3 + ……… + θn ∈ R.
(3) If z = r(cos θ + i sin θ) and n is a positive integer, then
No comments:
Post a Comment