3. For a curvey: [a, b] → C, define y: [a, b] → R² by y(t) = (Re(y(t)), Im(y(t)). For a function f : C → C, write f = u

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3 For A Curvey A B C Define Y A B R By Y T Re Y T Im Y T For A Function F C C Write F U 1 (21.04 KiB) Viewed 49 times

3. For a curvey: [a, b] → C, define y: [a, b] → R² by y(t) = (Re(y(t)), Im(y(t)). For a function f : C → C, write f = u + iv and define functions g,h: R² → R² by g(x, y) = (u(x, y),-v(x, y)) and h(x, y) = (v(x, y), u(x, y)). (3a) Write f g dy and fah-dy in terms of ffdz. • (3b) Prove that if f is entire, then g is conservative. (3c) If g is conservative, is f entire? Prove your answer.