Operaciones con numeros complejos i1450?

Es<img src="https://tex.z-dn.net/?f=%20i%5E%7B1450%7D%20" />

Primero recordemos :

<img src="https://tex.z-dn.net/?f=%20i%5E%7B1%7D%20" /> = i

<img src="https://tex.z-dn.net/?f=%20i%5E%7B2%7D%20" /> = - 1

<img src="https://tex.z-dn.net/?f=%20i%5E%7B3%7D%20" /> = - i

<img src="https://tex.z-dn.net/?f=%20i%5E%7B4%7D%20" /> = 1

Recuerda tambien que

<img src="https://tex.z-dn.net/?f=%20i%5E%7B4k%20%2B%201%7D%20" /> = <img src="https://tex.z-dn.net/?f=%20i%5E%7B1%7D%20" /> = i

<img src="https://tex.z-dn.net/?f=%20i%5E%7B4k%20%2B2%7D%20" /> = <img src="https://tex.z-dn.net/?f=%20i%5E%7B2%7D%20" /> = - 1

<img src="https://tex.z-dn.net/?f=%20i%5E%7B4k%20%2B3%7D%20" /> = [img = 10] = - i

[img = 11] = [img = 12] = 1

Dividimos 1450 entre 4 = 362 x 4 + 2

El 362 es como un multiplo de 4 osea es 4k

Entonces al dividir nos salio :

[img = 13] = [img = 14] = - 1

Rpta : - 1

Espero haberte ayudado : 3!