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

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Question : 52 of 52
Marks: +1, -0
If (1+i1−i)m\left(\frac{1+i}{1-i}\right)^m = 1 , then find the least positive integral value of m.
Solution:  
We have , (1+i1−i)m\left(\frac{1+i}{1-i}\right)^m = 1 ⇒ (1+i1−i×1+i1+i)m\left(\frac{1+i}{1-i} \times \frac{1+i}{1+i}\right)^m = 1
⇒ (1−1+2i1+1)m\left(\frac{1-1+2i}{1+1}\right)^m = 1 ⇒ (2i2)m\left(\frac{2i}{2}\right)^m = 1 ⇒ (i)m(i)^m = 1
⇒ m is multiple of 4.
∴ The least positive integral value of m is 4.
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