What names apply to the square root of 36?

The square root of - 36 is the square root of - 1 times the square root of + 36.

The answer is 6i, where i is the square root of - 1.

This can be checked by the standard formula for two complex numbers:

(a, b) x (c, d) = (ac-bd, ad+bc)

(0,6) x (0,6) = (0x0 - 6x6, 0x6 + 6x0) = (-36, 0) or just - 36