If $${\text{W}} = \phi + {\text{i}}\psi $$ represents the complex potential for an electric field. Given $$\psi = {{\text{x}}^2} - {{\text{y}}^2} + \frac{{\text{x}}}{{{{\text{x}}^2} + {{\text{y}}^2}}},$$ then the function $$\phi $$ is
A. $$ - 2{\text{xy}} + \frac{{\text{y}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$
B. $$2{\text{xy}} + \frac{{\text{y}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$
C. $$ - 2{\text{xy}} + \frac{{\text{x}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$
D. $$2{\text{xy}} + \frac{{\text{x}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$
Answer: Option A
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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