GATE IN 2005 | Complex Variable Question 7 | 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 2005

MCQ (Single Correct Answer)

-0.3

Let $${z^3}\, = \,\overline z $$, where z is a complex number not equal to zero. Then z is a solution of

$${z^2} = 1$$

$${z^3} = 1$$

$${z^4} = 1$$

$${z^9} = 1$$

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

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GATE IN Subjects

Engineering Mathematics

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