Complex Exponential

One of the most natural ways to express the function \(e^z\) in the complex plane is to use the Maclaurin series expansion with complex numbers. This website will visually show the terms in the series as vectors, using your pointer as input.

Some interesting things to notice:

• The series converges for all inputs
• When moving the cursor along the imaginary axis, the outputs are all on the unit circle
• There is no input which gives the origin as an output

Check out other things I'm working on.