An analytic function f(z) of complex variable z = x + iy may be written as f(z) = u(x, y) + iv(x, y). Then, u(x, y) and v(x, y) must satisfy,
A. $$\frac{{\partial {\text{u}}}}{{\partial {\text{x}}}} = \frac{{ - \partial {\text{v}}}}{{\partial {\text{y}}}}{\text{ and }}\frac{{\partial {\text{u}}}}{{\partial {\text{y}}}} = \frac{{\partial {\text{v}}}}{{\partial {\text{x}}}}$$
B. $$\frac{{\partial {\text{u}}}}{{\partial {\text{x}}}} = \frac{{ - \partial {\text{v}}}}{{\partial {\text{y}}}}{\text{ and }}\frac{{\partial {\text{u}}}}{{\partial {\text{y}}}} = \frac{{ - \partial {\text{v}}}}{{\partial {\text{x}}}}$$
C. $$\frac{{\partial {\text{u}}}}{{\partial {\text{x}}}} = \frac{{\partial {\text{v}}}}{{\partial {\text{y}}}}{\text{ and }}\frac{{\partial {\text{u}}}}{{\partial {\text{y}}}} = \frac{{ - \partial {\text{v}}}}{{\partial {\text{x}}}}$$
D. $$\frac{{\partial {\text{u}}}}{{\partial {\text{x}}}} = \frac{{\partial {\text{v}}}}{{\partial {\text{y}}}}{\text{ and }}\frac{{\partial {\text{u}}}}{{\partial {\text{y}}}} = \frac{{\partial {\text{v}}}}{{\partial {\text{x}}}}$$
Answer: Option C
This Question Belongs to Engineering Maths >> Complex Variable
A. -x2 + y2 + constant
B. x2 - y2 + constant
C. x2 + y2 + constant
D. -(x2 + y2) + constant
The product of complex numbers (3 - 2i) and (3 + i4) results in
A. 1 + 6i
B. 9 - 8i
C. 9 + 8i
D. 17 + 6i
If a complex number $${\text{z}} = \frac{{\sqrt 3 }}{2} + {\text{i}}\frac{1}{2}$$ then z4 is
A. $$2\sqrt 2 + 2{\text{i}}$$
B. $$\frac{{ - 1}}{2} + \frac{{{\text{i}}{{\sqrt 3 }^2}}}{2}$$
C. $$\frac{{\sqrt 3 }}{2} - {\text{i}}\frac{1}{2}$$
D. $$\frac{{\sqrt 3 }}{2} - {\text{i}}\frac{1}{8}$$
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