If `z=3- 4i` is turned `90^@` in anti clock direction then new position of z is

Vector z- 3-4i is rotated at 180 angle in anti clock wise direction and its length is increased to two and half xx.In new position z is

Ram is facing North -west . He turns in clockwise direction by 90^(@) , then 180^(@) in the anti- clock -wise direction and them another 90^(@) in the same direction and the another 90^(@) in the same direction . Which direction is he facing now ?

Rama is facing East. He turns 90° in clockwise direction, and then 135° in anti-clockwise direction and then again 90°in clockwise direction. Which direction is she facing now?

I am facing North. I turn 135°in clockwise direction, then 180°in anti-clockwise direction. What direction am I facing now?

The position vector of A is pbar(i)+bar(j). If A is rotated about O through an angle (pi)/(6) in anti clock wise direction.It coincides with B whose position vector bar(i)+qj. The value of p,q are

Let z_(1),z_(2),z_(3),z_(4) be the vertices A,B,C,D respectively of a square on the Argand diagramtaken in anticlockwise direction then prove that: 2z_(2)=(1+i)z_(1)+(1-i)z_(3)

If z_(1) , z_(2) and z_(3) are the vertices of DeltaABC , which is not right angled triangle taken in anti-clock wise direction and z_(0) is the circumcentre, then ((z_(0)-z_(1))/(z_(0)-z_(2)))(sin2A)/(sin2B)+((z_(0)-z_(3))/(z_(0)-z_(2)))(sin2C)/(sin2B) is equal to

In the Argand plane, the vector z = 4 - 3i is turned in the clockwise sense through 180^@ and stretched three times. The complex number represented by the new vector is

The complex number z=1+i is rotated through an angle (3 pi)/(2) in anti-clockwise direction about the origin and stretched by aditional sqrt(2) unit,then the new complex number is:

If the plane x+y+z=1 is rotated through 90^(@) about its line of intersection with the plane x-2y+3z=0, the new position of the plane is