How to convert sine to exponential form?

sinusoidalvoltage

In this question, he converted the sinusoidal voltage to exponential voltage.

what's the formula used here ? This is not the same one used in this video

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Here is the formula derived in the video

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Best Answer

I don't know about the video, but the Euler's relation

\$e^{jx} = \cos(x) + j\sin(x)\$

where j = \$\sqrt{-1}\$, x = \$ \omega t\$

...means that the real portion Re(j\$e^{j\omega t}\$) = -\$\sin(\omega t) \$ or Re(j\$e^{-j\omega t}\$) = \$\sin(\omega t) \$

So I think there are two things:

  1. Take the real part
  2. There is a missing minus sign in the book.
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