How do you graph x to the power of x with both the real and non-real parts?

Answer 1

To graph (x^x), you first need to understand that the function is only defined for positive values of x. The real part of the graph will resemble a curve that starts at (0,1) and increases rapidly as x increases. The non-real part of the graph will involve complex numbers, which can be visualized in the complex plane as spirals around the origin, with the spirals getting closer together as x increases.

Answer 2

This depends on what 'space' you want to plot it on. Another thing, are the x values all complex, or just real. I did a writeup on a similar question awhile back only considering real values of x, but complex values of y. For the positive sided, one way is to take the log of x^x, then you have log(y) = x*log(x). You can plot this manually on log paper.

If you use natural log, instead, then you have ln(y) = x*ln(x), then take e raised to both sides: y = e^(x*ln(x)).

To take natural log of a negative number, consider this:

if u = A*e^(iΘ), then ln(u) = ln(A) + (iΘ)*ln(e) = ln(A) + (iΘ)