Potencias de i
La unidad imaginaria i es definida como la raíz cuadrada de –1. Así, i 2 = –1.
i 3 puede ser escrito como ( i 2 ) i , que es igual a (–1) i o simplemente – i .
i 4 puede ser escrito como ( i 2 )( i 2 ), que es igual a (–1)(–1) o 1.
i 5 puede ser escrito como ( i 4 ) i , que es igual a (1) i o i .
Por lo tanto, el ciclo se repite cada cuatro potencias, como se muestra en la tabla.
|
Potencias de 10
|
|
| i 1 = i | i 0 = 1 |
| i 2 = –1 | i -1 = –i |
| i 3 = –i | i -2 = –1 |
| i 4 = 1 | i -3 = i |
|
i 5 = i |
i -4 = 1 |
|
i 6 = –1 |
i -5 = –i |
|
i 7 = –i |
i -6 = –1 |
|
i 8 = 1 |
i -7 = i |
|
i 9 = i |
i -8 = 1 |
|
etc. |
etc. |
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