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 minimum value of |z-1 if |z-3|-|z+1||=2

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

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

Factorize of the expression: a^(3)x+a^(2)(x-y)-a(y+z)-z

If z=x+iy(x,y in R,x!=-(1)/(2)), the number of values of z satisfying |z|^(n)=z^(2)|z|^(n-2)+z|z|^(n-2)+1(n in N,n>1) is

If x+y+z=1 , then the minimum value of xy(x+y)^(2)+yz(y+z)^(2)+zx(z+x)^(2) is , where x,y,z inR^(+)