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If ((1+i)/(1-i))^m=1, then find the leas...

If `((1+i)/(1-i))^m=1`, then find the least integral value of `m`

Text Solution

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`((1+ i)/(1-i))^(m) = 1`
or `(((1+i)^(2))/(1-i^(2)))^(m) = 1`
or ` ((1+ i^(2) +2i)/(2))^(m) = 1`
or `i^(m) = 1`
Therefore, the least positive integral value of m is 4.
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