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प्रश्न
If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.
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उत्तर
`((1+i)/(1-i))^m` = 1,
⇒ `((1+i)/(1-i) xx (1 + i)/(1 + i))^m` = 1,
⇒ `((1+ i)^2/(1^2 + 1^2))^m = 1`
⇒ `((1^2 + i^2 + 2i)/2)^2 = 1`
⇒ `((1 - 1 + 2i)/2)^2 = 1`
⇒ `((2i)/2)^m = 1`
⇒ `i^m = 1`
∴ m = 4k, where k is an integral
Therefore, the smallest positive integral is 1
Therefore, the least positive integral value of m is 4 (4 x 1).
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