Let `z_(1) and z_(2)` be two complex numbers such that `z_(1)//z_(2) + z_(2)//z_(1)=1`. Prove that `z_(1), z_(2)` and the origin form an equilateral triangle.

If z_(1) and z_(2) are non -zero complex numbers, then show that (z_(1) z_(2))^(-1)=z_(1)^(-1) z_(2)^(-1)

If z_(1) and z_(2) are two complex numbers satisfying the equation |(z_(1) + iz_(2))/(z_(1)-iz_(2))|=1 , then (z_(1))/(z_(2)) is

Let z_(1) and z_(2) be complex numbers satisfying |z_(1)|=|z_(2)|=2 and |z_(1)+z_(2)|=3 . Then |(1)/(z_(1))+(1)/(z_(2))|=

If z_(1) and z_(2) are complex numbers such that z_(1) ne z_(2) and |z_(1)|= |z_(2)| . If z_(1) has positive real part and z_(2) has negative imaginary part, then ((z_(1) +z_(2)))/((z_(1)-z_(2))) may be

If z_(1) and z_(2) are two non-zero complex numbers such that |z_(1) + z_(2)| = |z_(1)| + |z_(2)| , then arg ((z_(1))/(z_(2))) is equal to a)0 b) -pi c) -(pi)/(2) d) (pi)/(2)

For any two complex numbers z_1 and z_2 prove that Re(z_1z_2) = Re(z_1)Re(z_2) - Im(z_1)Im(z_2)

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