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Complex Variable

Engineering Mathematics

Previous Years Questions

Marks 1

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Let $$z=x+iy$$ where $$i = \sqrt { - 1} .$$ Then $$\overline {\cos \,z} = $$
GATE IN 2017
In the neighborhood of $$z=1,$$ the function $$f(z)$$ has a power series expansion of the form $$f\left( z \right) = 1 +...
GATE IN 2016
The value of the integral $${1 \over {2\pi j}}\int\limits_c {{{{z^2} + 1} \over {{z^2} - 1}}} dz$$ where $$z$$ is a com...
GATE IN 2016
The value of $$\oint\limits_c {{1 \over {{z^2}}}dz} $$ where the contour is the unit circle traversed clock - wise, is
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Let $$j\, = \,\sqrt { - 1} $$. Then one value of $${j^j}$$ is
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For the function $${{\sin z} \over {{z^3}}}$$ of a complex variable z, the point z = 0 is
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Let $${z^3}\, = \,\overline z $$, where z is a complex number not equal to zero. Then z is a solution of
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Consider the circle $$\left| {z\, - 5\, - 5i} \right|\, = \,2$$ in the complex number plane (x, y) with z = x + iy. The ...
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The bilinear transformation $$w\, = \,{{z\, - \,1} \over {z\, + \,1}}$$
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The complex number $$z\, = \,x\, + \,jy$$ which satisfy the equation $$\left| {z + 1} \right|\, = \,1$$ lie on
GATE IN 1997
$$\cos \phi $$ can be represented as
GATE IN 1994
The real part of the complex number $$z\, = \,x\, + \,iy$$ is given by
GATE IN 1994

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