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An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y)+ iv(x, y), where i = √-1. If u(x, y) = x2 - y2, then expression for v(x, y) in terms of x, y and a general constant c would be
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- xy + c
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x2 + y2 + c 2
- 2xy + c
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(x - y)2 + c 2
- xy + c
Correct Option: C
Given f(z) = μx(x, y) + iv (x, y) is analytic and x = x2 - y2
We know that if f(z) = μ + iv is analytic then C-R equations will be satisfied.
| i.e. | = | and | = - | ||||
| ∂x | ∂y | ∂y | ∂x |
∴ v = 2xy + c is correct answer
