easy calc question?

Question

Express (1-i)^8 in standard form

Answer 1

First, look at (1-i)^2, which is (1-i)(1-i). Which is 1*1-i-i+i^2. Note, i^2=-1. So, the equation is now 1-2i-1, or -2i.

Now, (1-i)^4 = ((1-i)^2)*((1-i)^2). By the previous answer, this is (-2i)*(-2i), which is -4(i^2), which is -4(-1), which is 4.

Now, (1-i)^8 = ((1-i)^4)*((1-i)^4). By the previous answer, this is 4*4, which is 16.

Answer 2

16

Answer 3

(1 - i)^8 =
((1 - i)^2)^4 =
(1 - 2i + i^2)^4 =
(1 - 2i - 1)^4 =
(-2i)^4 =
(-2)^4 (i)^4 =
16 * i^4 =
16 * 1 = 16