18.4 De Moivre's Theorem

]> 18.4 De Moivre's Theorem

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The variable $z, z = x + i y$ can be represented by its length and angle as can any two dimensional vector, and the relation as usual is

r^{2} = x^{2} + y^{2}

and

x = r \cos θ, y = r \sin θ

De Moivre's Theorem is the statement that $e^{θ} = \cos θ + i \sin θ$ . We can therefore write

z = x + i y = r e^{i θ}