If a function f(z) = u (x, y) + iv (x, y) of the complex variable z = x + iy, where x, y, u and v are real, is analytic in a domain D of z, then which of the following is true?

A) $$\frac{{\partial u}}{{\partial x}} = \frac{{\partial v}}{{\partial x}}$$ B) $$\frac{{\partial u}}{{\partial x}} = \frac{{\partial v}}{{\partial y}}{\text{ and }}\frac{{\partial u}}{{\partial y}} = - \frac{{\partial v}}{{\partial x}}$$ C) $$\frac{{\partial u}}{{\partial x}} = \frac{{\partial v}}{{\partial x}}{\text{ and }}\frac{{\partial u}}{{\partial y}} = \frac{{\partial v}}{{\partial y}}$$ D) $$\frac{{{\partial ^2}u}}{{\partial x\partial y}} = \frac{{{\partial ^2}v}}{{\partial x\partial y}}$$

Answer & Solution

Correct Answer: Option B

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If a function f(z) = u (x y) + iv (x...

If a function f(z) = u (x, y) + iv (x, y) of the complex variable z = x + iy, where x, y, u and v are real, is analytic in a domain D of z, then which of the following is true?

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