Given 9x² + 4 = 0

⇒ 9x² + 4 × 1 = 0

We have i² = –1 ⇒ 1 = –i²

By substituting 1 = –i² in the above equation, we get

9x² + 4(–i²) = 0

⇒ 9x² – 4i² = 0

⇒ (3x)² – (2i)² = 0

⇒ (3x + 2i)(3x – 2i) = 0 [∵ a² – b² = (a + b)(a – b)]

⇒ 3x + 2i = 0 or 3x – 2i = 0

⇒ 3x = –2i or 3x = 2i

Thus, the roots of the given equation are.