Exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the "base" and the "exponent" . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases:
Exponentiation
Another characterization of the exponential function formula_66 is as the limit of formula_75, as "n" approaches infinity. By thinking of the "n"th power in this definition as repeated multiplication in polar form, it can be used to visually illustrate Euler's formula. Any complex number can be represented in polar form as formula_76, where "r" is the absolute value and "θ" is its argument. The product of two complex numbers formula_77 and formula_78 is formula_79.