Given equation is x^{2} – (3√2 + 2i) x + 6√2 i = 0

Comparing with ax^{2} + bx + c = 0, we get

a = 1, b = -(3√2 + 2i), c = 6√2i

Discriminant = b^{2} – 4ac

= [-(3√2 + 2i)]^{2} – 4 × 1 × 6√2 i

= 18 + 12√2i + 4i – 24√2 i

= 18 – 12√2 i – 4 ……**[∵ i = -1**]

= 14 – 12√2 i

So, the given equation has complex roots.

These roots are given by

Equating real and imaginary parts, we get