The area of the triangle in the complex plane formed by the points z, iz and z+iz is

Show that the area of the triangle on the Argrand Diagram formed by the complex numbers z,iz and z+iz" "is" (1)/(2)|z|^(2).

The maximum area of the triangle formed by the complex coordinates z, z_1,z_2 which satisfy the relations |z-z_1|=|z-z_2| and |z-(z_1+z_2 )/2| |z_1-z_2| is

The area of the triangle whose vertices are represented by the complex numbers O,z and z(cos alpha + I sin alpha) (0 lt alpha lt pi) is equial to -

Let z=x+iy and omega=(1-iz)/(z-i). If |omega|=1 show the in the complex plane the point z lies on the real axis.

The coordiantes of the centroid of the triangle fromed by the points (x-y,y-z),(-x,-y)and(y,z) are -

The triangle formed by joining the points (x,y,z), (y,z,x) and (z,x,y) in three dimensional space is-

An equilateral triangle in the Argan plane has vertix as z_1 , z_2 and z_3 which are there complex no show that 1/(z_1-z_2)+1/(z_3-z_1)+1/(z_2-z_3)=0

Let A(z_1) and (z_2) represent two complex numbers on the complex plane. Suppose the complex slope of the line joining A and B is defined as (z_1-z_2)/(bar z_1-bar z_2) .If the line l_1 , with complex slope omega_1, and l_2 , with complex slope omeg_2 , on the complex plane are perpendicular then prove that omega_1+omega_2=0 .

The point z_1=3+sqrt(3)i and z_2=2sqrt(3)+6i are given on a complex plane. The complex number lying on the bisector of the angle formed by the vectors z_1a n dz_2 is a. z=((3+2sqrt(3)))/2+(sqrt(3)+2)/2i b. z=5+5i c. z=-1-i d.none of these

If z^4=(z-1)^4 , then the roots are represented in the Argand plane by the points that are: