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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