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BITSAT 2014
Exam
BITSAT
Year
2014
Subject
Mathematics
Chapter
Complex Number

BITSAT 2014 · Mathematics · Complex Number

i^ 57 + 1 i^ 25 , when simplified has the value

i57+1i25,i^{57}+\frac{1}{i^{25}}, when simplified has the value

Options

  1. A0
  2. B2i2 i
  3. C−2i-2 i
  4. D2

Correct answer

A. 0

Step-by-step solution

i57+1i25=(i4)14⋅i+1(i4)6⋅i=i+1i(∵i4=1)=i−i(∵1i=−i)=0\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}
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