Question

Números Complexos:
Efetue:

a) (2+i)$^{2}$ - i.(2+i).(2-i) =

b) (1+4)$^{4}$ =

c) (1+i)$^{5}$ . (1-i)$^{5}$ =

Answer 1

a) (2+i) - i.(2+i).(2-i) = 4 + 4i + i^2 -[ 4 - i^2] = 4 + 4i + i^2 - 4 + i^2
4 - 1 + 4i - 4 - 1 
 - 2 + 4i ==> -2(1 - 2i)

b) (1+4i) = (1+4i)^4 ==> (1+4i)^0 ==> (1+4i)^1 ==> 1 + 4i

c) (1+i) . (1-i) = (1+i)(1-i) ==> 1 - i^2 ==> 1+1 ==> 2