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In previous formulas, {{tmath|x, y, t}} ae commonly interpreted as real variables, but the formulas remain valid if the variables are interpreted as complex variables. These formulas may be used for defining trigonometric functions of a complex variable.<ref name="Apostol_1974"/>
===Plots===▼
<gallery caption="3D plots of real part, imaginary part, and modulus of the exponential function" class="center" mode="packed" style="text-align:left" heights="150px">
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Starting with a color-coded portion of the <math>xy</math> ___domain, the following are depictions of the graph as variously projected into two or three dimensions.
▲===Plots===
<gallery class="center" mode="packed" style="text-align:left" heights="200px" caption="Graphs of the complex exponential function">
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