Exponential function: Difference between revisions

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==Complex exponential==

{{anchor|On the complex plane|Complex plane}}

[[File:The exponential function e^z plotted in the complex plane from -2-2i to 2+2i.svg|alt=The exponential function e^z plotted in the complex plane from -2-−2 − 2i to 2 + 2i|thumb|The exponential function e^z plotted in the complex plane from -2-−2 − 2i to 2 + 2i]]

[[Image:Exp-complex-cplot.svg|thumb|right|A [[Domain coloring|complex plot]] of <math>z\mapsto\exp z</math>, with the [[Argument (complex analysis)|argument]] <math>\operatorname{Arg}\exp z</math> represented by varying hue. The transition from dark to light colors shows that <math>\left|\exp z\right|</math> is increasing only to the right. The periodic horizontal bands corresponding to the same hue indicate that <math>z\mapsto\exp z</math> is [[periodic function|periodic]] in the [[imaginary part]] of <math>z</math>.]]