If `z_(1),z_(2),z_(3)` are the vertices `A,B,C` of a right angled triangle taken in counte-clockwise direction with right angle at `B` and `(AC)/(BC)=sqrt(5)` ,then `(z_(3)-z_(2))=`

z_(1),z_(2),z_(3) are the vertices of an equilateral triangle taken in counter clockwise direction. If its circumcenter is at (1-2i) and (z_(1)=2+i) , then z_(2)=

If z_(1),z_(2),z_(3) are the vertices of an isoscles triangle right angled at z_(2) , then

z_(1),z_(2),z_(3) are the vertices of an equilateral triangle taken in counter clockwise direction. If its circumference is at the origin and z_(1)=1+i , then

If z_(1) , z_(2) and z_(3) are the vertices of DeltaABC , which is not right angled triangle taken in anti-clock wise direction and z_(0) is the circumcentre, then ((z_(0)-z_(1))/(z_(0)-z_(2)))(sin2A)/(sin2B)+((z_(0)-z_(3))/(z_(0)-z_(2)))(sin2C)/(sin2B) is equal to

If z_(1),z_(2),z_(3),z_(4), represent the vertices of a rhombus taken in anticlockwise order,then

Complex numbers z_(1),z_(2),z_(3) are the vertices A,B,C respectively of an isosceles right angled trianglewith right angle at C and (z_(1)-z_(2))^(2)=k(z_(1)-z_(3))(z_(3)-z_(2)) then find k.

Complex numbers z_(1),z_(2)andz_(3) are the vertices A,B,C respectivelt of an isosceles right angled triangle with right angle at C. show that (z_(1)-z_(2))^(2)=2(z_1-z_(3))(z_(3)-z_(2)).

Complex numbers of z_(1),z_(2),z_(3) are the vertices A, B, C respectively, of on isosceles right-angled triangle with right angle at C. show that (z_(1) - z_(2))^(2) = 2 (z_(1) - z_(3)) (z_(3)- z_(2))

If z_(1),z_(2),z_(3) are vertices of an equilateral triangle inscribed in the circle |z|=2 and if z_(1)=1+iota sqrt(3), then