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.
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.