Pollard Klein
09/13/2024 · Primary School
\( i ^ { q } = \)
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La expresión \( i^q \) se refiere a la potencia de la unidad imaginaria \( i \), donde \( i = \sqrt{-1} \). La potencia de \( i \) sigue un patrón cíclico:
- \( i^1 = i \)
- \( i^2 = -1 \)
- \( i^3 = -i \)
- \( i^4 = 1 \)
Después de \( i^4 \), el ciclo se repite. Por lo tanto, para calcular \( i^q \), puedes usar el residuo de \( q \) al dividirlo entre 4:
- Si \( q \equiv 0 \mod 4 \), entonces \( i^q = 1 \)
- Si \( q \equiv 1 \mod 4 \), entonces \( i^q = i \)
- Si \( q \equiv 2 \mod 4 \), entonces \( i^q = -1 \)
- Si \( q \equiv 3 \mod 4 \), entonces \( i^q = -i \)
Así que el resultado de \( i^q \) depende del valor de \( q \) y su residuo al dividir entre 4.
Quick Answer
El resultado de \( i^q \) depende del valor de \( q \) y su residuo al dividir entre 4.
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