Please simplify this equation

3i^3 - 3√-16 + 3i^2

Please show your work and explain. THANKS!

3i^3 - 3√-16 + 3i^2
= 3i^3 - 3(√16)(√-1) + 3i^2
= 3i^3 - 12i + 3i^2
= 3i² × i - 12i + 3i^2
= – 3 × i - 12i – 3
= – 15i – 3
-----

ok, so you have to know that i = root of (-1)

i^2 = -1 that is (root of -1)^2

i^3 is nothing but (i^2)*(i), right ? that is (i squared)*(i)

therefore i^3 is (-1)(i) since i^2 = -1

therefore i^3 = -i

so using this, i^3 becomes (-i) and i^2 becomes (-1)

= 3*(-i) - 3i*(root of 16) + 3*(-1) : i split (root of -16) into (root of -1)*(root of 16)

=-3i - 3i*4 -3 : basic simplification

= -3i -12i - 3 : taking - 3 out common

= -3(i - 4i - 1) = -3(5i - 1)

Note: i^2 = -1
3i^3 - 3√-16 + 3i^2
= 3i^2*i -3sqrt(i^2(4)^2 + 3i^2
=- 3i - 3*4i +3(-1)
=- 3i - 12i - 3
=- 15i-3
=- 3(5i+1) <= ans

-3i - 12i - 3 = -3 (5i + 1) That's it..:D

i^3 = -i
√-16 = i√16 = 4i
i^2 = -1