(1+i)^5.(1-i)^5
(1+i)^5 =
(1+i)² . (1+i)² . (1+i) =
(1² + 2i + i²) . (1² + 2i + i²) . (1+i) =
(1 + 2i -1) . (1 + 2i -1) .(1+i) =
(2i) . (2i) . (1+i) =
4i² . (1+i) =
-4 .(1+i) =
-4 - 4i
(1-i)^5 =
(1-i)² . (1-i)² . (1-i) =
(1² - 2i + i²) . (1² -2i +i²) . (1-i) =
(1 - 2i -1) . (1-2i -1) .(1-i) =
(-2i) . (-2i) . (1-i) =
4i² . (1-i) =
-4 . (1-i) =
-4 + 4i =
(-4 - 4i) . (-4 + 4i) =
16 - 16i + 16i - 16i² =
16 + 16 =
32
