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

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Question : 3 of 52
Marks: +1, -0
i−39i^{-39}
Solution:  
i−39i^{-39} = 1i39\frac{1}{i^{39}} = 1(i2)19⋅i\frac{1}{(i^2)^{19} \cdot i} = 1(−1)19⋅i\frac{1}{(-1)^{19} \cdot i} [Since i2i^2 = - 1]
= 1(−1)⋅i\frac{1}{(-1) \cdot i} = 1−i\frac{1}{-i} = −1i×ii-\frac{1}{i} \times \frac{i}{i} = −ii2-\frac{i}{i^2} = −i−1\frac{-i}{-1} = i = 0 + 1i
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