Question from sofia, a parent:

Compute the given arithmetic expression and give the answer in the form a + bi where a,b element in R. 1. (1 - i)^5

Hi Sofia,

I am going to work with 3 - 2i.

(3 - 2i)^{2} = 3^{2} - 12i + (-2i)^{2} = 9 - 12i + 4i^{2} = 9 - 12i - 4 = 5 - 12i (3 - 2i)^{3} = (5 - 12i)(3 - 2i) = 15 - 46i + (-12i)(-2i) = 15 - 46i + 24i^{2} = 15 - 46i - 24 = -9 - 46i (3 - 2i)^{5} = (3 - 2i)^{2}(3 - 2i)^{3} = (5 - 12i)(-9 - 46i) = ···

(3 - 2i)^{2} = 3^{2} - 12i + (-2i)^{2} = 9 - 12i + 4i^{2} = 9 - 12i - 4 = 5 - 12i

(3 - 2i)^{3} = (5 - 12i)(3 - 2i) = 15 - 46i + (-12i)(-2i) = 15 - 46i + 24i^{2} = 15 - 46i - 24 = -9 - 46i

(3 - 2i)^{5} = (3 - 2i)^{2}(3 - 2i)^{3} = (5 - 12i)(-9 - 46i) = ···

Now you try (1 - i)^{5}

Harley