I have a composition of 7 functions I need simplified into its real and imaginary parts. I have tried many of the suggestions on different posts such as ComplexExpand, ReIm, but none of them seem to work. Any suggestions on what to try? I am new to Mathematica, so apologies if there are other simple mistakes. Also, Mathematica is so awesome, I wish I knew about it earlier.
Thanks in advance, and here are the functions.
f1[z_] = 2 (-I*z + 6 I)/(z) f2[z_] = (pi/2) (I*z + 1) f3[z_] = sin[z] f4[z_] = z^2 C = sin[3 I]^2 D = sin[(pi/2) + I*pi]^2 f5[z_] = ( (C - D)/C)*(z/(D - z) ) f6[z_] = Sqrt[z] f7[z_] = (2/pi)*arcsin[z] G[z_] = Composition[f7, f6, f5, f4, f3, f2, f1][z] G[2 + 2 I] G