Respuesta:
Por reducción
A = 1
Explicación paso a paso:
A = (i²⁰ + i³² + i¹⁰⁰) / (i⁶⁰ + i⁸⁰ + i¹⁰²⁴)
A = i²⁰(1 + i¹² + i⁸⁰) / i²⁰(i⁴⁰ + i⁶⁰ + i¹⁰⁰⁴)
A = (1 + i¹² + i⁸⁰) / (i⁴⁰ + i⁶⁰ + i¹⁰⁰⁴)
Por definción i² = (-1)
A = (1 + (i²)⁶ + (i²)⁴⁰) / ((i²)²⁰ + (i²)³⁰ + (i²)⁵⁰²)
A = (1 + (-1)⁶ + (-1)⁴⁰) / ((-1)²⁰ + (-1)³⁰ + (-1)⁵⁰²)
A = (1 + 1 + 1) / (1 + 1 + 1)
A = 3 / 3
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Respuesta:
Por reducción
A = 1
Explicación paso a paso:
A = (i²⁰ + i³² + i¹⁰⁰) / (i⁶⁰ + i⁸⁰ + i¹⁰²⁴)
A = i²⁰(1 + i¹² + i⁸⁰) / i²⁰(i⁴⁰ + i⁶⁰ + i¹⁰⁰⁴)
A = (1 + i¹² + i⁸⁰) / (i⁴⁰ + i⁶⁰ + i¹⁰⁰⁴)
Por definción i² = (-1)
A = (1 + (i²)⁶ + (i²)⁴⁰) / ((i²)²⁰ + (i²)³⁰ + (i²)⁵⁰²)
A = (1 + (-1)⁶ + (-1)⁴⁰) / ((-1)²⁰ + (-1)³⁰ + (-1)⁵⁰²)
A = (1 + 1 + 1) / (1 + 1 + 1)
A = 3 / 3
A = 1