`z_1a n dz_2` are the roots of `3z^2+3z+b=0.` if `O(0),(z_1),(z_2)` form an equilateral triangle, then find the value of `bdot`

If z_1a n dz_2 are conjugate to each other then find a r g(-z_1z_2)dot

If 2a x-2y+3z=0,x+a y+2z=0,a n d2+a z=0 have a nontrivial solution, find the value of adot

If z_1a n dz_2 are the complex roots of the equation (x-3)^3+1=0,t h e nz_1+z_2 equal to a. 1 b. 3 c. 5 d. 7

Suppose z_(1),z_(2)andz_(3) are the vertices of an equilateral triangle inscribed in the circle |z| = 2. If z_(1)=1+isqrt3 then find z_(2)andz_(3) .

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

If the points A(z),B(-z),a n dC(1-z) are the vertices of an equilateral triangle A B C , then (a)sum of possible z is 1/2 (b)sum of possible z is 1 (c)product of possible z is 1/4 (d)product of possible z is 1/2

If a rg(z_1)=170^0a n d arg(z_2)=70^0 , then find the principal argument of z_1z_2dot

If z=omega,omega^2w h e r eomega is a non-real complex cube root of unity, are two vertices of an equilateral triangle in the Argand plane, then the third vertex z may be represented by (a) z=1 b. z=0 c. z=-2 d. z=-1

It is given that complex numbers z_1a n dz_2s a t i sfy|z_1|=22a n d|z_2|=3. If the included angled of their corresponding vectors is 60^0 , then find the value of |(z_1+z_2)/(z_1-z_2)| .