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Complex exponential function

The complex exponential function is one-valued and is defined as

where z = a + bi.

 


Explanation

The function is often written as

ex+i y = ex (cos y + i sin y)

and has names like Euler's formula, De Moivre's formula. Also the cis function describes an exponential function.

 


Power series

The power series for the exponential function can be written as

 


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