I want to add that any formula that contains exponentials of real arguments, e^x, and/or exponentials of imaginary arguments, e^(i*x), can be rewritten by using only binary exponentials, 2^x, and/or unary exponentials, 1^x, both having only real arguments.
With this substitution, some formulae become simpler and others become more complicated, but, when also considering the cost of the function evaluations, an overall greater simplicity is achieved.
In comparison with the "e" based exponentials, the binary exponential and the unary exponential and their inverses have the advantage that there are no rounding errors caused by argument range reduction, so they are preferable especially when the exponents can be very big or very small, while the "e" based exponentials can work fine for exponents guaranteed to be close to 0.
With this substitution, some formulae become simpler and others become more complicated, but, when also considering the cost of the function evaluations, an overall greater simplicity is achieved.
In comparison with the "e" based exponentials, the binary exponential and the unary exponential and their inverses have the advantage that there are no rounding errors caused by argument range reduction, so they are preferable especially when the exponents can be very big or very small, while the "e" based exponentials can work fine for exponents guaranteed to be close to 0.