If `|z_1-z_0|=|z_2-z_0|=a` and `amp((z_2-z_0)/(z_0-z_1))=pi/2` , then find `z_0`

If |z_(1)+z_(2)|=|z_1|+|z_2| then

If |z_1/z_2|=1 and arg (z_1z_2)=0 , then

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.

|z_(1)|=|z_(2)|" and "arg z_(1)+argz_(2)=0 then

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( barz )_2dot

Let z_1 and z_2 be two distinct complex numbers and let z=(1-t)z_1+t z_2 for some real number t with 0 (a) |z-z_1|+|z-z_2|=|z_1-z_2| (b) arg(z-z_1)=arg(z-z_2) (c) (z-z_1) bar(z_2-z_1) = bar (z-z_1)(z_2-z_1) (d) a r g(z-z_1)=a r g(z_2-z_1) .

Let z_1, z_2, z_3 be the three nonzero complex numbers such that z_2!=1,a=|z_1|,b=|z_2|a n d c=|z_3|dot Let |(a, b, c), (b, c, a), (c,a,b) |=0 a r g(z_3)/(z_2) equal to (a) arg((z_3-z_1)/(z_2-z_1))^2 (b) orthocentre of triangle formed by z_1, z_2, z_3, i sz_1+z_2+z_3 (c)if triangle formed by z_1, z_2, z_3 is equilateral, then its area is (3sqrt(3))/2|z_1|^2 (d) if triangle formed by z_1, z_2, z_3 is equilateral, then z_1+z_2+z_3=0

If z_(1)=2-i, z_(2)=1+i , find |(z_(1)+z_(2)+1)/(z_(1)-z_(2)+1)| .