Question

(1+i)^5.(1-i)^5 essa esquaça~o levada a potençia 5

Answer 1

(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