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The expression cos x + i sin x is abbreviated with cis x and is therefore only another name for Euler's formula



Trigonometric functions can be defined with complex numbers.


For each real number x, Euler's formula applies in the form

Here e is the base of the natural logarithm, i is the imaginary unit, and in the sine and cosine x are expressed in radians. The general form of the complex exponential function is


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