Answer to Question #173750 in Complex Analysis for Rayhan

Question #173750

For two real numbers x and yf(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) (xy)^2



1
Expert's answer
2021-03-31T14:26:07-0400

"((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.


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