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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} $$where the contour is the unit circle traversed clock - wise, is GATE IN 2015 Let$$j\, = \,\sqrt { - 1} $$. Then one value of$${j^j}$$is GATE IN 2007 For the function$${{\sin z} \over {{z^3}}}$$of a complex variable z, the point z = 0 is GATE IN 2007 Let$${z^3}\, = \,\overline z $$, where z is a complex number not equal to zero. Then z is a solution of GATE IN 2005 Consider the circle$$\left| {z\, - 5\, - 5i} \right|\, = \,2$$in the complex number plane (x, y) with z = x + iy. The ... GATE IN 2005 The bilinear transformation$$w\, = \,{{z\, - \,1} \over {z\, + \,1}}$$GATE IN 2002 The complex number$$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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