Answer to Question #173750 in Complex Analysis for Rayhan

Question

For two real numbers x and y, f(x+iy) can be written as u(x,y)+iv(x,y) where u and v are functions of real variables.

 What is ((x+1)^2+y^2)u(x,y)?

a) (x+1)^2+y^2

b) x^2+y^2−1

c) y^2−x^2+1

d) (x−y)^2

Answer 1

$((x + 1)^2 + y^2) u(x, y)$

$(x^2 + 2 x + y^2 + 1) u(x, y)$

$y^2 u(x, y) + (x + 1)^2 u(x, y)$

$x^2 u(x, y) + y^2 u(x, y) + 2 x u(x, y) + u(x, y)$

$d/dx(((x + 1)^2 + y^2) u(x, y)) = ((x + 1)^2 + y^2) u^(1, 0)(x, y) + 2 (x + 1) u(x, y)$

$(x+1)^2+y^2$

Option A is Correct.