Evaluate z :

`( 1 - iotasqrt3 )^2 / ( ( 1 + iotasqrt3 ) ( 1 - iotasqrt3 ) )`

If the complex number z_1,z_2 and z_3 represent the vertices of an equilateral triangle inscribed in the circle |z|=2 and z_1=1+isqrt(3) then (A) z_2=1,z_3=1-isqrt(3) (B) z_2=1-isqrt(3),z_3=-isqrt(3) (C) z_2=1-isqrt(3), z_3=-1+isqrt(3) (D) z_2=,z_3=1-isqrt(3)

Find the value of (( x -y )^3 + ( y - z )^3 + ( z - x )^3 )/ (9 ( x - y )( y - z ) ( z - x )) 1 . 0 2 . 1/9 3 . 1/3 4. 1

If z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i| = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals to : a) 3sqrt(3) b) sqrt(3) c) 3 d) 1/(3sqrt(3))

Given w = - 2, x = 3, y = 0 & z = - (1)/(2) . Find the value of (z)/(w) + x . A. 3 (1)/(4) B. - 3 (1)/(4) C. 3.2 D. 3.5

(i) Find the equations of the straight line passing through the point (2,3,-1) and is perpendicular to the lines : ( x-2)/(2) = (y + 1)/(1) = (z - 3)/(-3) and (x - 3)/(1) = (y + 2)/(1) = (z - 1)/(1) . (ii) Find the equation of the line which intersects the lines : (x + 2)/(1) = (y - 3)/(2) = (z + 1)/(4) and (x - 1)/(2) = (y - 2)/(3) = (z - 3)/(4) Perpendicular and passes through the point (1,1,1) .

If z_1 = 3i and z_2 = -1 -i , find the value of arg z_1/z_2 .

Find the S.D. between the lines : (i) (x)/(2) = (y)/(-3) = (z)/(1) and (x -2)/(3) = (y - 1)/(-5) = (z + 4)/(2) (ii) (x -1)/(2) = (y - 2)/(3) = (z - 3)/(2) and (x + 1)/(3) = (y - 1)/(2) = (z - 1)/(5) (iii) (x + 1)/(7) = (y + 1)/(-6) = (z + 1)/(1) and (x -3)/(1) = (y -5)/(-2) = (z - 7)/(1) (iv) (x - 3)/(3) = (y - 8)/(-1) = (z-3)/(1) and (x + 3)/(-3) = (y +7)/(2) = (z -6)/(4) .

Evaluate x^3+y^3+z^3-3xyz when x=2, y=-1 and z=3.