write the expression in form of a+bi
(-2-3i)(1+4i)
multiply just like any other polynomial
(-2-3i)(1+4i) = -2(1+4i) - 3i(1+4i)
= -2 - 8i - 3i - 12i^2
but recall that i^2 = -1, so you wind up with
-2 -11i + 12 = 10 - 11i
(-2-3i)(1+4i)
(-2-3i)(1+4i) = -2(1+4i) - 3i(1+4i)
= -2 - 8i - 3i - 12i^2
but recall that i^2 = -1, so you wind up with
-2 -11i + 12 = 10 - 11i