Let `z_(1), z_(2), z_(3)` be three complex numbers and a, b, c be real numbers not all zero such that `a+b+c= 0 and az_(1) + bz_(2) +cz_(3)= 0`. Show that `z_(1), z_(2), z_(3)` are collinear.

z_(1) and z_(2) be two complex numbers with alpha and beta as their principal arguments, such that alpha + beta gt pi , then principal Arg (z_(1) z_(2)) is

If z_(1)=2+3i and z_(2)=3+2i , then |z_(1)+z_(2)| is equal to

If z_(1), z_(2),……..,z_(n) are complex numbers such that |z_(1)| = |z_(2)| = …….. = |z_(n)| = 1 , then |z_(1) + z_(2) +……..+ z_(n)| is equal to a) |z_(1)z_(2)z_(3)…..z_(n)| b) |z_(1)|+|z_(2)|+…….+|z_(n)| c) |(1)/(z_(1)) + (1)/(z_(2)) + ……….+ (1)/(z_(n))| d)n

Let x_1 and y_1 be real numbers. If z_1 and z_2 are complex numbers such that |z_1| = |z_2|=4 , then |x_1 z_1 - y_1 z_2|^(2) + |y_1 z_1 + x_1 z_2 |^(2) is equal to

If the complex numbers z _(1) , z _(2) and z _(3) denote the vertices of an isosceles triangle, right angled at z _(1), then (z _(1) - z _(2)) ^(2) + (z _(1) - z _(3)) ^(2) is equal to A)0 B) (z _(2) + z _(3)) ^(2) C)2 D)3

If z_(1), z_(2), z_(3) are three complex numbers and A= |("arg"z_(1),"arg"z_(2),"arg"z_(3)),("arg"z_(2),"arg"z_(3),"arg"z_(1)),("arg"z_(3),"arg"z_(1),"arg"z_(2))| then A is divisible by

Given that for any complex number z, absz^2 = zoverlinez . Prove that abs(z_1+z_2)^2 + abs(z_1-z_2)^2 = 2[abs(z_1)^2 + abs(z_2)^2] where z_1 and z_2 are any two complex numbers.