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

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^(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

Let z_1 , z _2 and z_3 be three complex numbers such that z_1 + z_2+ z_3 = z_1z_2 + z_2z_3 + z_1 z_3 = z_1 z_2z_3 = 1 . Then the area of triangle formed by points A(z_1 ), B(z_2) and C(z_3) in complex plane is _______.

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,z_4 be the vertices of a quadrilaterla taken in order such that z_1+z_2=z_2+z_3 and |z_1-z_3|=|z_2-z_4| then arg ((z_1-z_2)/(z_3-z_2))= (A) pi/2 (B) +- pi/2 (C) pi/3 (D) pi/6

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|=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 :

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

Let z_(1),z_(2),z_(3) be three distinct complex numbers satisfying |z_(1)-1|=|z_(2)-1|=|z_(3)-1|* If z_(1)+z_(2)+z_(3)=3 then z_(1),z_(2),z_(3) must represent the vertices of