Question

question 5
0.83 pts
what is the solution of the equation when solved over the complex numbers?
x² + 27 = 0
select both answers
□ 3√3
□ 3i√3
□ -3√3
□ -3i√3

Explanation:

Step1: Isolate \(x^2\)

Start with the equation \(x^2 + 27 = 0\). Subtract 27 from both sides:
\(x^2 = -27\)

Step2: Apply square root property

Take the square root of both sides. Recall that \(\sqrt{-a} = i\sqrt{a}\) for \(a > 0\).
\(x = \pm\sqrt{-27}\)

Step3: Simplify \(\sqrt{-27}\)

Simplify \(\sqrt{-27}\) as \(i\sqrt{27}\). Then, \(\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}\). Thus:
\(\sqrt{-27} = 3i\sqrt{3}\)

Step4: Write both solutions

From \(x = \pm\sqrt{-27}\), the solutions are \(x = 3i\sqrt{3}\) and \(x = -3i\sqrt{3}\).

Answer:

B. \(3i\sqrt{3}\), D. \(-3i\sqrt{3}\)