Find the circumstance of the triangle whose vertices are given by the complex numbers `z_(1),z_(2)` and `z_(3)`.

If two triangles whose vertices are respectively the complex numbers z_(1),z_(2),z_(3) and a_(1),a_(2),a_(3) are similar, then the determinant. |{:(z_(1),a_(1),1),(z_(2),a_(2),1),(z_(3),a_(3),1):}| is equal to

The area of the triangle whose vertices are represented by the complex numbers O,z and iz 'where z is (cos alpha + i sin alpha) is equial to -

Find the perimeter of a triangle whose sides are 2y+3z, z-y, 4y-2z .

Find the coordinates of the centroid of the triangle whose vertices are (x_1,y_1,z_1) , (x_2,y_2,z_2) and (x_3,y_3,z_3) .

Show that the area of the triangle on the Argand diagram formed by the complex numbers z, zi and z+ zi is =(1)/(2) |z|^(2)

If z is a complex number such that |z|=2 , then the area (in sq. units) of the triangle whose vertices are given by z, -iz and iz-z is equal to

If z is a complex number, then the area of the triangle (in sq. units) whose vertices are the roots of the equation z^(3)+iz^(2)+2i=0 is equal to (where, i^(2)=-1 )

If z_(1), z_(2), z_(3) are three complex numbers representing three vertices of a triangle, then centroid of the triangle be (z_(1) + z_(2) + z_(3))/(3)

A,B and C are the points respectively the complex numbers z_(1),z_(2) and z_(3) respectivley, on the complex plane and the circumcentre of /_\ABC lies at the origin. If the altitude of the triangle through the vertex. A meets the circumcircle again at P, prove that P represents the complex number (-(z_(2)z_(3))/(z_(1))) .

Let z_(0) be the circumcenter of an equilateral triangle whose affixes are z_(1),z_(2),z_(3) . Statement-1 : z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=3z_(0)^(2) Statement-2: z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=2(z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1))