Other Complex Functions
Power functions are not the only interesting complex functions (just as
real power functions are not the only interesting real functions). Two
other important ones are the exponential and logarithm functions. Just as
was the case for the squaring and square root functions and the cubing and
cube roots functions, these two are two different views of a single
function graph; they are inverse relations for each other.
Given a complex number z = x + yi, the
exponential of z is given by ez =
excosy +
exsiny i. The logarithm is
simply the inverse relation for this function.
For the examples below, we use a rectangular domain where -1 <
x < 1 and -2pi < y
< 2pi. We use a hypercube with edge length 10 to
better match this domain.
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The complex exponential function
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The complex logarithm function
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