e^(jωt) /e^-(jωt), What do these means in terms of coding?

Question

What does e^jωt / e^-jωt mean in terms of coding?

I know it is e^jωt = cos(ωt)+jsin(ωt). But if you have it in terms of an algorithm how do you program it?

Answer 1

There's a special function to raise e to a power, called exp. So you want:

exp(j*w*t)

Or:

exp(-j*w*t)

To use this function you'll need to #include <math.h>, and when compiling on Linux systems add the -lm flag to link the math library.

EDIT:

If j is the imaginary unit, you can use the cexp function to raise e to a complex power:

cexp(I*w*t)

You can store the result in a variable of type double complex and use the creal and cimag functions to extract the real and imaginary parts. Also, you 'll need to #include <complex.h>

Answer 2

As you say, e^(jωt) = cos(ωt)+jsin(ωt)

While e^(-jωt) = cos(ωt)-jsin(ωt) <- sign-change for second term

Therefore, e^(jωt) / e^(-jωt)

is simply

( cos(ωt)+jsin(ωt) ) / ( cos(ωt)-jsin(ωt) )

You may find the following paper useful. http://web.mit.edu/6.02/www/s2007/lec3.pdf