Q48 / 125 · BITSAT 2014 · Mathematics

$i^{57}+\frac{1}{i^{25}},$ when simplified has the value

  • Correct answer
    A
    0
  • B
    $2 i$
  • C
    $-2 i$
  • D
    2

Solution

$\begin{aligned} i^{57}+\frac{1}{i^{25}}=\left(i^{4}\right)^{14} \cdot i &+\frac{1}{\left(i^{4}\right)^{6} \cdot i} \\=i+\frac{1}{i}\left(\because i^{4}=1\right) &=i-i\left(\because \frac{1}{i}=-i\right) \\ &=0 \end{aligned}$

Hence, the correct answer is option: 'A'.

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