Question

Boa tarde... (números complexos) @)Calcule o valor das expressões a)4i^57-2i^39+7i^125 b)i^100-i^101+i^102-i^103​

Answer 1

Resposta: -1 e 0

os potencias de i

i^(4k + 0) = i^0 = 1

i^(4k + 1) = i^1 = i

i^(4k + 2) = i^2 = -1

i^(4k + 3) = i^3 = -1

passo-a-passo:

a)

4i^57 - 2i^39 +7i^125

57 = 56 + 1

39 = 36 + 3

125 = 124 + 1

= 4i + 2i + 7i = 13i

b)

i^100 - i^101 + i^102 - i^103​

100 = 4*25 + 0

101 = 4*25 + 1

102 = 4*25 + 2

103 = 4*25 + 3

= 1 - I - 1 + I = 0