Find the minimum value of the expression `E= |z|^2+ |z-3|^2 + |z- 6i|^2` (where `z=x+iy, x,y in R`)

Find the least value of the expression x^(2) + 4y^(2) + 3z^(2) - 2x - 12y -6z + 14

Solve :z+|z|=1+2i , where z=x+iy,x,yinRR .

Find the locus of z if |3z - 5 | = 3 |z + 1| where z = x + iy

If xyz = 1 and x, y, z gt 0 then the minimum value of the expression (x+2y)(y+2z)(z+2x) is

If xyz = 1 and x, y, z gt 0 then the minimum value of the expression (x+2y)(y+2z)(z+2x) is

The value of the expression ((x ^(2) - y ^(2)) ^(3) + ( y ^(2) - z ^(2)) ^(3) + (z ^(2) - x ^(2)) ^(3))/((x - y) ^(3) + ( y - z) ^(3) + (z - x ) ^(3)) is

The set of points on the complex plane such that z^(2)+z+1 is real and positive (where z=x+iy,x,y in R) is

Solve the equation |z|+z=2+i, where z = x + iy.

If 2x+3y+6z=14 then the minimum value of x^(2)+y^(2)+z^(2) is