Exercise "complex"

Calculate, using our cmath class, √-1, √i, eⁱ, e^iπ, iⁱ, ln(i), sin(iπ) and compare with manually calculated results.

Extra: add to our cmath-class the hyperbolic functions sinh, cosh of complex argument—and calculate sinh(i), cosh(i). Check that the results are correct.

Hints:

• System.Math.E ≈ e, System.Math.PI ≈ π, cmath.I ≈ i.
• Install wget,

  sudo apt install wget

  Then

  cd /path/to/my/complex/class/files

  and get the complex.cs and cmath.cs files,

  wget http://80.251.205.75/~fedorov/prog/matlib/complex/complex.cs
  wget http://80.251.205.75/~fedorov/prog/matlib/complex/cmath.cs
  

• Add the following lines to your Makefile to build the cmath.dll library,

  CMATHDIR = /path/to/my/complex/class/files
  cmath.dll : $(CMATHDIR)/cmath.cs $(CMATHDIR)/complex.cs
  	mcs -target:library -out:./cmath.dll $^ # note "./" in front of cmath.dll
  

• Read the source code complex.cs and cmath.cs to find out how the complex numbers and complex function are defined.
• Create a main.cs file with the "Main" method that solves the exercise.
• Link with your "cmath.dll" library when compiling your main.cs,

  main.exe : main.cs cmath.dll
  	mcs -reference:cmath.dll main.cs