Given equation is x^{2} + 4ix – 4 = 0

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

a = 1, b = 4i, c = -4

Discriminant = b^{2} – 4ac

= (4i)^{2} – 4 × 1 × (-4)

= 16i^{2} + 16

= -16 + 16 ….**.[∵ i = -1]**

= 0

So, the given equation has equal roots.

These roots are given by

∴ x = -2i

∴ The root of the given equation is -2i.