# Working with complex functions and complex conjugation

I have a complex function and I want to take a list of derivatives of it. My code reads as follows:

$Assumptions[w>0] f[r, t] = Exp[-I wt] (It Exp[-I wr]/r + R Exp[I w r]/r) ComplexExpand[Conjugate[f[r, t]]]  In my function, I want the coefficients It and R to be complex numbers. However, this gives me the following output: (R Cos[r w] Cos[wt])/r + (It Cos[wr] Cos[wt])/r + (R Sin[r w] Sin[wt])/r - (It Sin[wr] Sin[wt])/r + I (-((R Cos[wt] Sin[r w])/r) + (It Cos[wt] Sin[wr])/r + (R Cos[r w] Sin[wt])/r + (It Cos[wr] Sin[wt])/r  This treats It and R as real numbers and it expands the exponentials using Euler's identity. How do I get the conjugate of the functions in a simpler form, and taking It and R as complex. • REad the manual about "ComplexExpand" and you will see that you need to indicate which variables are complex. Oct 25, 2021 at 8:11 • That still returns everything in terms of Sin and Cos even though the input is in terms of exponentials. The complex numbers themselves are also expressed as Re[] and Im[]. Is there some kind of z z^* style notation available? Oct 25, 2021 at 8:20 • Look at "TrigToExp" Oct 25, 2021 at 10:14 • Hard to tell if you mean wr or w*r in your code since you have it both ways. It puts what you mean bywt in doubt also. Jul 22 at 21:46 ## 1 Answer $Assumptions[w > 0]
f[r, t] = Exp[-I w t] (It Exp[-I w r]/r + R Exp[I w r]/r)
ce = ComplexExpand[Conjugate[f[r, t]], {It, R},
TargetFunctions -> Conjugate] // Simplify