2x² – (3 + 7i)x + (9i – 3) = 0

Given 2x² – (3 + 7i)x + (9i – 3) = 0

Recall that the roots of quadratic equation ax² + bx + c = 0, where a ≠ 0, are given by

Here, a = 2, b = –(3 + 7i) and c = (9i – 3)

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

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

We can write 16 + 30i = 25 – 9 + 30i

⇒ 16 + 30i = 25 + 9(–1) + 30i

⇒ 16 + 30i = 25 + 9i² + 30i [∵ i² = –1]

⇒ 16 + 30i = 5² + (3i)² + 2(5)(3i)

⇒ 16 + 30i = (5 + 3i)² [∵ (a + b)² = a² + b² + 2ab]

By using the result 16 + 30i = (5 + 3i)², we get

[∵ i² = –1]

Thus, the roots of the given equation are 3i and.