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Polar form writes z = r(cos θ + i sin θ) = re^(iθ). Powers become trivial in this form: the modulus is raised to the power and the argument is multiplied by it, which is De Moivre's theorem.
Polar form
z = r(cos θ + i sin θ) = r·e^(iθ)
De Moivre
zⁿ = rⁿ(cos nθ + i sin nθ)
The modulus is 4.2426407 and the argument 45°, so the fourth power has modulus 324 and argument 180° — that is −324.
It turns multiplication into addition of exponents, which is why it dominates electrical engineering and wave physics.