Q66 / 100 · BITSAT 2023 (Memory Based Paper 1) · 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

$i^{57}+\frac{1}{i^{25}}=\left(i^4\right)^{14} . i+\frac{1}{\left(i^4\right)^6 .i}=i+\frac{1}{i}=i-i=0$

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

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