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Given z6 + 1 = (z2 + 1)(z2 −√3 z + 1)(z2 + √3 z + 1). Divide both sides of this identity by z3, and then let z = cis to show that: cos 3θ = 4 cosθ (cos(θ) − cos(π/6) )(cos(θ) − cos (5π/6) )

Given z6 + 1 = (z2 + 1)(z2 −√3 z + 1)(z2 + √3 z + 1). Divide both sides of this identity by z3, and then let z = cis to show that: cos 3θ = 4 cosθ (cos(θ) − cos(π/6) )(cos(θ) − cos (5π/6) )

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Given z6 + 1 = (z2 + 1)(z2 −√3 z + 1)(z2 + √3 z + 1).

Divide both sides of this identity by z3, and then let z = cis to show that:

cos 3θ = 4 cosθ (cos(θ) − cos(π/6) )(cos(θ) − cos (5π/6) )

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