What are the roots of the equation x^2-4x+13=0?

Hello : 
x² -4x +13  = 0
(x²-2(2)(x) +2²) -2² +13 = 0
(x-2)² +9 = 0
in : R no solution reals
in:C two solutions :
x-2 =3i  or x-2 = -3i
x =2+3i   or x = 2-3i   because : - 9 = 9i² = (3i)²  i² = -1

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