Suppose that f is a function of the complex variable z = x + iy given
by
f(x + iy) = (x^3 - axy^2 + 2x^2 - 2by^2 + 1) + i(cyx^2 - y^3 + dxy)
for some real constants a; b; c; d. It is known that f is entire. What are
the constants a; b; c; d?
Suppose that f is a function of the complex variable z = x + iy given
by
f(x + iy) = (x^3 - axy^2 + 2x^2 - 2by^2 + 1) + i(cyx^2 - y^3 + dxy)
for some real constants a; b; c; d. It is known that f is entire. What are
the constants a; b; c; d?
I would suggest that you look at the "Cauchy-Riemann" equations that must be satified at every z.