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Pre-calculus?
I need some help figuring out a trigonometric question regarding DeMoivre's Theorem.
The question is: Use DeMoivre's Theorem to find the indicated power of the complex number.
[radical5(cos pi/15 + isin pi/15)]^4
1 Answer
- ?Lv 75 years ago
=>
De Moivre's Theorem
z = r(cos θ + i sin θ) => polar vector form: z = x + y i
r = √(x^2 + y^2)
z₁ = r₁(cos θ₁ + i sin θ₁)
z₂ = r₂(cos θ₂ + i sin θ₂)
z₁*z₂ = r₁*r₂[cos(θ₁+θ₂) + i sin(θ₁+θ₂)]
z₁/z₂ = r₁/r₂[cos(θ₁-θ₂) + i sin(θ₁-θ₂)]
zⁿ = rⁿ (cos nθ + i sin nθ) => when z = r(cos θ + i sin θ)
....................................................
z = √5(cos π/15 + i sin π/15)
n=4, θ = π/15
[√5(cos π/15 + i sin π/15)]^4
= (√5)^4 (cos 4π/15 + i sin 4π/15)
= 25 (cos 4π/15 + i sin 4π/15)
