Exponential form is a representation using exponentiation, with distinct uses for equations involving logarithms and for complex numbers.
For a positive base 
, the exponential form of the relation 
is
 |
where 
and 
is real. It is equivalent to the logarithmic
form of the same relation (Abramson 2021). For example, 
is the exponential form of 
.
The exponential form of a nonzero complex number is
 |
where 
is its complex modulus and 
is a complex argument.
By the Euler formula, this is equivalent to the
polar form 
. The complex
argument is determined only modulo 
(Churchill and Brown 1990).
