Question

What is the solution of the equation when solved over the complex numbers?

Answer 1

Try this option:

x²+27=0;

$(x+\sqrt{-27})(x- \sqrt{-27})=0; \ => \ \left[\begin{array}{ccc}x=3 \sqrt{3}i\\x=-3 \sqrt{3}i \end{array}\right$

Answer 2

x = ± 3i√3

given x² + 27 = 0 (subtract 27 from both sides )

x² = - 27 ( take the square root of both sides )

x = ±$\sqrt{-27}$ = ± √(9 × 3 × -1 ) ← (i = √-1 )

  = ± (√9 × √3  ×√-1 ) = ±3i√3