Exercise "math"

1. Calculate (using System.Math and/or our cmath classes): √2, eⁱ, e^iπ, iⁱ, sin(iπ) and check that the results are correct.
2. Extra: add to our cmath-class the hyperbolic functions sinh, cosh and the functions sqrt and abs—of complex argument—and calculate sinh(i), cosh(i), sqrt(-1), sqrt(i). Check that the results are correct.

Hints:

• Look at the lectures/math example.
• System.Math.E ≈ e, System.Math.PI ≈ π.
• Read the source code cmath.cs to find out how the complex function are defined.
• Get the complex.cs and cmath.cs files and place them in the directory of your math-exercise,

  wget http://62.107.14.89/~fedorov/prog/lib/complex/complex.cs
  wget http://62.107.14.89/~fedorov/prog/lib/complex/cmath.cs
  

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

  cmath.dll : cmath.cs complex.cs
  	mcs -target:library -out:cmath.dll cmath.cs complex.cs
  

  If you put the files in another directory, say /path/to/my/lib, than the lines should be modified slightly,

  LIBDIR = /path/to/my/lib
  cmath.dll : $(LIBDIR)/cmath.cs $(LIBDIR)/complex.cs
  	mcs -target:library -out:cmath.dll $^
  

  Link this library when compiling your main.cs,

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