Question

Calculo de numeros complexos. Calcule: i2000+i2002?

Answer 1

Olá, Mar3gabrunaClara.

$i^{2000}+i^{2002}=i^{2\cdot1000}+i^{2\cdot1001}=(i^2)^{1000}+(i^2)^{1001}=\\\\=(-1)^{1000}+(-1)^{1001}=(-1)^{1000}\cdot[1+(-1)]=\\\\=(-1)^{1000}\cdot0=\\\\=\huge{\boxed{0}}$

Answer 2

Resolução:
i² = -1
i²⁰⁰⁰ + i²⁰⁰²
(i²)¹⁰⁰⁰ + (i²)¹⁰⁰¹
(-1)¹⁰⁰⁰ + (-1)¹⁰⁰¹   
1 + (-1)
1 - 1
  0
bons estudos.