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# Complex exponentials spin

When we put time in the exponent of a complex exponential, the complex number it represent rotates in a circle on the complex plane. You can think of it as a spinning number! Created by Willy McAllister.

## Want to join the conversation?

• When we have a negative number in the exponent here, why don't put it over one? example e to the power of negative 1j is one over e to the 1j power?
(1 vote)
• You can write the exponential that way if you want, 1/e^jwt. But you won't see that done in most texts. The emphasis is not on the reciprocal nature of the number. Instead, we use the negative exponent because in the neighborhood somewhere there is always a similar exponential term with a + sign in the exponent. You want to be able to visually see that pair of numbers and clump them together.
(1 vote)
• why is he using w for omega instead of Ω