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Am I right, that the following is the so-called trigonometric form of the complex number $c \in \mathbb{C}$?

$|c| \cdot (\cos \alpha + \mathbf{i} \sin \alpha)$

And the following is the Euler form of the very same number, right?

$|c|\cdot \mathbf{e}^{\mathbf{i}\alpha}$

I think there must be a mistake in one of my tutor's notes..

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For the second one I don't know if it's called Euler Form but perhaps the name comes from Euler's Formula $e^{i\theta} = \cos \theta + i \sin \theta$. – user38268 Jan 22 '12 at 14:42
yes. The second version is often named 'exponential form'. – Raymond Manzoni Jan 22 '12 at 14:44
polar form of complex number – pedja Jan 22 '12 at 14:44

They are the same, and can also be called "polar coordinates" for the complex number.

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@GEdar, if in one exercise is asked to write the solutions of an equation in Euler form, is it the same if I write them in polar / trigonometric form? I mean, Euler form and polar / trigonometric form stand exactly for the same representation of the complex numbers? I know how to convert a complex number from rectagular to trigonometric form but it is the first time that I hear about the Euler form – Always learning Oct 24 '15 at 14:50

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