GATE IN 2005 | Complex Variable Question 8 | Engineering Mathematics

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

GATE IN 1994

MCQ (Single Correct Answer)

-0.3

The real part of the complex number $$z\, = \,x\, + \,iy$$ is given by

$${\mathop{\rm Re}\nolimits} (z)\, = \,z\, - \,{z^*}$$

$${\mathop{\rm Re}\nolimits} (z)\, = \,{{z\, - \,{z^*}} \over 2}$$

$${\mathop{\rm Re}\nolimits} (z)\, = \,{{z\, + \,{z^*}} \over 2}$$

$${\mathop{\rm Re}\nolimits} (z)\, = \,z\, + \,{z^*}$$

GATE IN Subjects

Engineering Mathematics