A particle starts to travel from a point P on the curve `C_1:|z-3-4i|=5`, where `|z|` is maximum. Form P, the particle moves through an angle `tan^-1 (3/4)` in anticlockwise direction on `|z-3-4i|=5` and reaches at point Q. From Q it comes down parallel to imaginary axis by 2 units and reachpoint R. Find the complex number corresponding to point R in the Argand plane.

Show that complex numbers z_1=-1+5i and z_2=-3+2i on the argand plane.

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

If (z + 3)/( z - 5i) = ( 1 + 4i)/(2) find the complex number z.

A point z moves on the curve |z-4-3i| =2 in an argand plane. The maximum and minimum values of z are

A point z moves on the curve |z-4-3i|=2 in an argand plane.The maximum and minimum values of z are

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 in the direction of the vector hati+hatj and then it moves through an angle pi/2 in anticlockwise direction on a circle with center at origin, to reach a point z_(2) . The point z_(2) is given by

In the Argand plane, the points represented by the complex numbers 2-6i ,4-7i, 3 - 5i and 1 - 4i 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 (a) 6+7i (b) -7+6i (c) 7+6i (d) -6+7i