`|z +3| <= 3`, then the greatest and least value of `|z + 1|` are

If |z-3i|=|z+3i| , then find the locus of z.

Let z_(1), z_(2), z_(3) be three complex numbers such that |z_(1)| = |z_(2)| = |z_(3)| = 1 and z = (z_(1) + z_(2) + z_(3))((1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))) , then |z| cannot exceed

Prove that traingle by complex numbers z_(1),z_(2) and z_(3) is equilateral if |z_(1)|=|z_(2)| = |z_(3)| and z_(1) + z_(2) + z_(3)=0

z_(1),z_(2) and z_(3) are the vertices of a triangle ABC such that |z_(1)|=|z_(2)|=|z_(3)| and AB=AC. Then ((z_(1)+z_(3))(z_(1)+z_(2)))/((z_(2)+z_(3))^(2)) is

If complex numbers z_(1)z_(2) and z_(3) are such that |z_(1)| = |z_(2)| = |z_(3)| , then prove that arg((z_(2))/(z_(1)) = arg ((z_(2) - z_(3))/(z_(1) - z_(3)))^(2)