To simplify the expression (-1 + 3i)/(1 + i)^6, we first need to simplify the denominator.

Given (a + bi)(a - bi) = a^2 - b^2i^2, we have:

(1 + i)(1 - i) = 1 - i^2 = 1 - (-1) = 1 + 1 = 2

Therefore, the denominator simplifies to 2^6 = 64.

Now, we have:

(-1 + 3i)/64
= (-1/64) + (3i/64)
= -1/64 + 3i/64
= (1 - 3i)/64

So, the simplified expression is (1 - 3i)/64.