GATE IN
Engineering Mathematics
Complex Variable
Previous Years Questions

## Marks 1

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