`A(z_1),B(z_2),C(z_3)` are the vertices of he triangle `A B C` (in anticlockwise). If `/_A B C=pi//4` and `A B=sqrt(2)(B C)` , then prove that `z_2=z_3+i(z_1-z_3)dot`

A(z_1),B(z_2),C(z_3) are the vertices of the triangle A B C (in clockwise). If /_A B C=pi//4 and A B=sqrt(2)(B C) , then prove that z_2=z_3+i(z_1-z_3)dot

z_1, z_2a n dz_3 are the vertices of an isosceles triangle in anticlockwise direction with origin as in center , then prove that z_2, z_1a n d kz_3 are in G.P. where k in R^+dot

On the Argand plane z_1, z_2a n dz_3 are respectively, the vertices of an isosceles triangle A B C with A C=B C and equal angles are thetadot If z_4 is the incenter of the triangle, then prove that (z_2-z_1)(z_3-z_1)=(1+sectheta)(z_4-z_1)^2dot

Let z_1, z_2a n dz_3 represent the vertices A ,B ,a n dC of the triangle A B C , respectively, in the Argand plane, such that |z_1|=|z_2|=|z_3|=5. Prove that z_1sin2A+z_2sin2B+z_3sin2C=0.

In A B C ,A(z_1),B(z_2),a n dC(z_3) are inscribed in the circle |z|=5. If H(z_n) be the orthocenrter of triangle A B C , then find z_ndot

If the points A(z),B(-z),a n dC(1-z) are the vertices of an equilateral triangle A B C , then (a)sum of possible z is 1/2 (b)sum of possible z is 1 (c)product of possible z is 1/4 (d)product of possible z is 1/2

If the complex numbers z_(1), z_(2)" and "z_(3) denote the vertices of an isoceles triangle, right angled at z_(1), " then "(z_(1)-z_(2))^(2)+(z_(1)-z_(3))^(2) is equal to

If z_1, z_2, z_3 be the affixes of the vertices A, B Mand C of a triangle having centroid at G such ;that z = 0 is the mid point of AG then 4z_1 + Z_2 + Z_3 =

Let vertices of an acute-angled triangle are A(z_1),B(z_2),a n dC(z_3)dot If the origin O is he orthocentre of the triangle, then prove that z_1( bar z )_2+( bar z )_1z_2=z_2( bar z )_3+( bar z )_2z_3=z_3( bar z )_1+( bar z )_(3)z_1