Expressing $g(z)=3x^2+2x-3y^2-1+i(6xy+2y)$ as a function of $z$. Would like hints on what direction to begin? The closest I got was $f(z)=3z^2=3x^2-3y^2+i6xy$, but I am missing 3 terms. How do I do this more systematically? Note that I have set $z=x+iy$.
2026-04-02 21:47:30.1775166450
Expressing a complex function $f(x,y)$ as $f(z)$.
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You're well on your way! Now, look at the terms you haven't yet written as a function of $z$: $$ g(z)-f(z)=2x-1+i\cdot2y $$ Can you express that as a function in $z$, say $h(z)$? If so, then we have $$ g(z)-f(z)=h(z)\\ g(z)=f(z)+h(z) $$ and you're done.