GATE IN 2005 | Complex Variable Question 8 | Engineering Mathematics

GATE IN 2005

MCQ (Single Correct Answer)

-0.3

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 origin to the circle is

$$5\sqrt 2 - 2$$

$$\sqrt {54} $$

$$\sqrt {34} $$

$$5\sqrt 2 $$

GATE IN 2002

MCQ (Single Correct Answer)

-0.3

The bilinear transformation $$w\, = \,{{z\, - \,1} \over {z\, + \,1}}$$

maps the inside of the unit circle in the z-plane to left half of the w - plane

maps the outside of the unit circle in the z-plane to left half of the w - plane

maps the inside of the unit circle in the z-plane to right half of the w - plane

maps the outside of the unit circle in the z-plane to right half of the w - plane

GATE IN 1997

MCQ (Single Correct Answer)

-0.3

The complex number $$z\, = \,x\, + \,jy$$ which satisfy the equation $$\left| {z + 1} \right|\, = \,1$$ lie on

a circle with ( 1, 0 ) as the center and radius 1

a circle with ( - 1, 0 ) as the center and radius 1

y-axis

x-axis

GATE IN 1994

MCQ (Single Correct Answer)

-0.3

$$\cos \phi $$ can be represented as

$${{{e^{i\phi }}\, - \,{e^{ - i\phi }}} \over 2}$$

$${{{e^{i\phi }}\, - \,{e^{ - i\phi }}} \over {2i}}$$

$${{{e^{i\phi }}\, + \,{e^{ - i\phi }}} \over i}$$

$${{{e^{i\phi }}\, + \,{e^{ - i\phi }}} \over 2}$$

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Calculus Complex Variable Linear Algebra Probability and Statistics Numerical Methods Transform Theory Differential Equations Vector Calculus