complex function

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• August 17th 2009, 04:20 PM
arbolis
complex function
I must rewrite the function $f$ in the form $f(z)=u(x,y)+iv(x,y)$ where $f(z)=z^3+z-1$.

What I did was to write $z$ as $x+iy$ and I found out that $f(z)=\overbrace{x^3-3xy^2+x-1}^{u(x,y)}+i\overbrace{(y-y^3+3x^2y)}^{v(x,y)}$.
Assuming I didn't do any arithmetic error, is my approach right?
• August 17th 2009, 05:14 PM
Plato
Looks good.