Below I tried to describe a complex polynomial which is a part of my newton method. When I define the complex number x, for example x = new ComplexNumber (0,0), it doesn't return the right value. Also I have overriden the basic string format to make it look like a complex number, but it doesn't show. It does show if I perform an arithmic operation like when I test a method. As a beginner I am clueless.

btw all methods for the complex arithmetic operations are defined and tested, ComplexNumber(real part, imaginary part)

note: My first attempt I tried to split the polynomial into a real and an imaginary part, but that doesn't work well when the root is also a complexnumber... So I moved on to the above.

Please go through that expression and work out what sort of algebraic formula it corresponds to. Use a pencil and paper and work from right to left; every time you reach a dot put round brackets () around your expression. See whether that gives the correct formula.
I don't understand the bit about "String". Do you mean what you get when you print the ComplexNumber to screen?