Logarithms and Powers
Some mathematical identities taught in school are not universally true, but only apply for certain values of the variables. Plotting them over the complex plane makes it easy to see where they hold, and where they do not.
The identity is true only if . See http://functions.wolfram.com/ElementaryFunctions/Log/16/05/.
Plot both forms to verify that they are the same on the right half-plane but different on the left.
A similar result holds for the "identity" .