Editing Exponential function (section)

===Relationship with trigonometry===
Complex exponential and [[trigonometric function]]s are strongly related by [[Euler's formula]]:
<math display="block">e^{it} =\cos(t)+i\sin(t). </math>

This formula provides the decomposition of complex exponential into [[real and imaginary parts]]:
<math display="block">e^{x+iy} = e^x\,\cos y + i e^x\,\sin y.</math>

The trigonometric functions can be expressed in terms of complex exponentials:
<math display="block">\begin{align}
\cos x &= \frac{e^{ix}+e^{-ix}}2\\
\sin x &= \frac{e^{ix}-e^{-ix}}{2i}\\
\tan x &= i\,\frac{1-e^{2ix}}{1+e^{2ix}}
\end{align}</math>

In these formulas, {{tmath|x, y, t}} are commonly interpreted as real variables, but the formulas remain valid if the variables are interpreted as complex variables. These formulas may be used to define trigonometric functions of a complex variable.<ref name="Apostol_1974"/>