evaluated anticlockwise around the circle |z - i| = 2, where is
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Engineering Maths · all questionsComplex Variable
Complex Variable
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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,
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In the neighborhood of z = 1, the function f(z) has a power series expansion of the form
Then f(z) is
Then f(z) is
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Solutions of Laplace equation having continuous second-order partial derivatives are called
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Square roots of -i, where are
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Given two complex numbers and the argument in degree is
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The value of the contour integral in the complex plane along the contour |z| = 3, taken counter-clockwise is
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In the Laurent expansion of valid in the region 1 < | z | < 2, the coefficient of is
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If then the value of xx is
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For an analytic function, f(x + iy) = u(i, y) + iv(i, y), u is given by u = 3x2 - 3y. The expression for v, considering K to be a constant is
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The real part of an analytic function f(z) where z = x + jy is given by e-y cos(x). The imaginary part of f(z) is
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