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