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NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

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Question : 52
Total: 52
If (
1+i
1−i
)m = 1 , then find the least positive integral value of m.
Solution:  
We have , (
1+i
1−i
)m = 1 ⇒ (
1+i
1−i
×
1+i
1+i
)m = 1
⇒ (
1−1+2i
1+1
)m = 1 ⇒ (
2i
2
)m = 1 ⇒ (i)m = 1
⇒ m is multiple of 4.
∴ The least positive integral value of m is 4.
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