If `z-1/z=2`, then `z^3-1/z^3=?`

If 2z_(1)-3z_(2)+z_(3)=0, then z_(1),z_(2) and z_(3) are represented by

If z_(1)=iz_(2) and z_(1)-z_(3)=i(z_(3)-z_(2)), then prove that |z_(3)|=sqrt(2)|z_(1)|

If |z_1|=1, |z_2|=2, |z_3|=3 and |9z_1z_2 + 4z_1z_3 + z_2z_3|=36 , then |z_1+z_2+z_3| is equal to :

If z^(2)-z+1=0, then the value of (1)/(12)[(z+(1)/(z))^(2)+(z^(2)+(1)/(z^(2)))^(2)+(z^(3)+(1)/(z^(3)))^(2)+.........(x^(24)+(1)/(z^(24)))^(2)] is equal to

If |z_1=1,|z_2|=2,|z_3|=3 and |z_1+z_2+z_3|=1, then |9z_1z_2+4z_3z_1+z_2z_3| is equal to (A) 3 (B) 36 (C) 216 (D) 1296

If z_1 z_2 = 5 & z_1^3 z_2^3 = 20 15 i then |z_1^4 z_2^4| is equal to

If z_1,z_2,z_3 are complex numbers such that |z_1|=z_2|=|z_3|=|z_1+z_2+z_3|=1, then (1/z_1+1/z_2+1/z_3| is (A) equal to 1 (B) les than (C) greater than 3 (D) equal to 3

If z_1, z_2, z_3 are the points A, B, C in the Argand Plane such that 1/(z_2-z_3)+1/(z_3-z_1)+1/(z_1-z_2)=0 , Prove that ABC is an equilateral triangle .

If |z_(1)|=|z_(2)|=|z_(3)| and z_(1)+z_(2)+z_(3)=0 , then z_(1),z_(2),z_(3) are vertices of

If |z_1|=2, |z_2|=3, |z_3|=4 and |2z_1+3z_2 + 4z_3|=9 , then value of |8z_2z_3 + 27z_3z_1 + 64z_1z_2|^(1//3) is :