Let `z_(1),z_(2) and z_(3)` be non-zero complex numbers satisfying `z^(2)=bar(iz), where i=sqrt(-1).`
What is `z_(1)+z_(2)+z_(3)` equal to ?

Find the non-zero complex numbers z satisfying z=iz^(2)

Let z_(1),z_(2) and z_(3) be non-zero complex numbers satisfying z^(2)=bar(iz), where i=sqrt(-1). Consider the following statements: 1. z_(1)z_(2)z_(3) is purely imaginary. 2. z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1) is purely real. Which of the above statements is/are correct?

If z_(1), z_(2) are two non-zero complex numbers satisfying |z_(1)+z_(2)|=|z_(1)|+|z_(2)| , show that Arg z_(1) - Arg z_(2)=0

Let z_(1), z_(2), z_(3) be three non-zero complex numbers such that z_(1) bar(z)_(2) = z_(2) bar(z)_(3) = z_(3) bar(z)_(1) , then z_(1), z_(2), z_(3)

Let z_(1),z_(2),z_(3),z_(4) are distinct complex numbers satisfying |z|=1 and 4z_(3) = 3(z_(1) + z_(2)) , then |z_(1) - z_(2)| is equal to

Let z_(1),z_(2),z_(3),z_(4) are distinct complex numbers satisfying |z|=1 and 4z_(3) = 3(z_(1) + z_(2)) , then |z_(1) - z_(2)| is equal to

Let z = x + iy be a non - zero complex number such that z^(2) = I |z|^(2) , where I = sqrt(-1) then z lies on the :

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)- arg. z_(2) equals :