testing exp(log(z))=z ... ...passed
testing log(exp(z))=z ... ...passed
testing abs(z)^2=z*conj(z) ... ...passed
testing sqrt(a)*sqrt(a)=a ... ...passed
testing sin(a)^2+cos(a)^2=1 ... ...passed
testing sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b) ... ...passed
testing (a/b)*b=a ... ...passed
testing exp(a+b)=exp(a)*exp(b) ... ...passed
testing cos(a+b)=cos(a)*cos(b)-sin(a)*sin(b) ... ...passed
testing abs(z)*exp(I*arg(z))=z ... ...passed
all tests passed :)