A square circumscribes the circle `|z -1| = sqrt2`. If one of the vertices represents the complex number `2 + isqrt3` then find the complex numbers represented by the other vertices.

Represent the complex number z=1+i sqrt(3) in the polar form.

Represent the complex number z=1+isqrt3 in polar form.

If z^2 = 12 sqrt(-1) , find the complex number z .

Convert the complex number 4/(1-isqrt3) in the polar form.

If |z|=2 then the points representing the complex number -1+5z will be

If |z|=2, the points representing the complex numbers -1+5z will lie on

If z_1,z_2 are two complex numbers representing two consecutive vertices of a square then what is the complex number represented by the centre of the square ?

If |z| =2 then then the complex number 1/z is represented on a fixed ________.

If the complex numbers z_1, z_2, z_3, z_4 taken in that order, represent the vertices of a rhombus, then

z_1,z_2 are represented by two consecutive vertices of a rhombus, the angle at z_1 being pi/4 . Find the complex numbers z_3,z_4 represented by the other vertices, the vertices z_1,z_2,z_3,z_4 being in the anticlockwise sense and origin being the center.