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

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The correct Answer is:
30
Let `z = x + iy`
`therefore E =zbarz+ (z-3)(barz -3)+(z-6i) (barz + 6i)`
`= 3zbarz -3(z+barz) +9+6(z-barz)i+36`
`=3(x^(2) +y^(2)) -x -12y + 45`
`=3(x^(2) + y^(2) - 2x -4y + 15 ]`
`= 3[(x-1)^(2) + (y-2)^(2) + 10]`
`therefore E_("min") = 30` when `x= 1` and y = 2
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