Eulers formel

Eulers formel är en elegant omskrivning av komplexa tal och det medför också det mest vackra sambandet som går att finna inom matematik nämligen kopplingen mellan talen, e, π, i och -1.
Allmän Eulers formel: \[ a+bi= r \cdot (cos v + i \cdot sin v ) =r \cdot e^{iv}) \]

Ett exempel på en omskrivning med Eulers formel: \[ 4+4i= \sqrt{32} \cdot (cos \frac{\pi}{4} + i \cdot sin \frac{\pi}{4} ) =\sqrt{32} e^{\frac{\pi i}{4} }) \].
Tveklöst är det så att det uttrycket längst till höger är mer elegant än uttrycket i mitten.
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