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What is the smallest positive integer n, for which (1 + i)2n = (1 – i)2n?

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प्रश्न

What is the smallest positive integer n, for which (1 + i)2n = (1 – i)2n?

योग
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उत्तर

n = 2, Because (1 + i)2n = (1 – i)2n  ⇒ `((1 + i)/(1 - i))^(2n)` = 1

⇒ (i)2n = 1 Which is possible if n = 2   ......(∴ i4 = 1)

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अध्याय 5: Complex Numbers and Quadratic Equations - Solved Examples [पृष्ठ ८७]

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एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
अध्याय 5 Complex Numbers and Quadratic Equations
Solved Examples | Q 20 | पृष्ठ ८७

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