If a complex number `z = 1 + sqrt3i` is rotated through an angle of `120^@` in anticlockwise direction about origin and reach at `z_1,` then `z_1` is

If a complex number z=1+sqrt(3)i is rotated through an angle of 120^(@) in anticlockwise direction about origin and reach at z_(1), then z_(1) is

The complex number z =1 + i is rotated through an angle 3pi//2 in anticlock wise direction about the origin and stretched by sqrt2 times , then the new complex number 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:

The complex number 3-4i is rotated by 90^(@) in the anticlockwise direction about origin. The complex number in new position is

A particle starts from a point z_0=1+i where i=sqrt(-1). lt moves horizontally away from origin by 2 units and then vertically away from origin by 3 units to reach a point z_1, From z_1 particle moves sqrt5 units in the direction of 2hat i+3hatj and then it moves through à n angle of cosec^(-1) 2 in anticlockwise direction of a circle with centre at origin to reach a point z_2. The arg z_1 is given by

Represent the complex numbers z= 1 + sqrt3i into polar form

A particle P starts from the point z_0=1+2i , where i=sqrt(-1) . It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z_1dot From z_1 the particle moves sqrt(2) units in the direction of the vector hat i+ hat j and then it moves through an angle pi/2 in anticlockwise direction on a circle with centre at origin, to reach a point z_2dot The point z_2 is given by

Represent the complex number z=1+sqrt3i in the polar form.