Real and Imaginary Parts of z+(1/z) - Have I Got This Right?

[kingyof2thejring]

Hi there have i got this right if someone could check please? $$z=x+\imath{}y$$ Find the real and imaginary parts $$z+(1/z)$$ sub $$x+\imath{}y + \frac{1}{x+\imath{}y}$$ if we multiply by $$x+\imath{}y$$ and i get as the real part as $$x^2-y^2+1$$. Have i got this right? Thanks in advance

 

[Hammie]

No. First step.. I'd deal with the fractional part. Multiply the numerator and denominator by the complex conjugate of the denominator, and simplify. That's how you divide by a complex number anyway..

 

[kingyof2thejring]

cheers mate