15 - Complex Trigonometric Functions

The exponential changes a bit for a complex number, taking on the form of

The complex exponential satisfies all properties of the real exponetial, with two new additions, first, the modulus of the complex exponential is the exponential to the real part of that complex number,
Another property that the complex exponential satisfies is that the exponential of a complex conjugate is equivalent to the conjugate of the exponential of that complex number,