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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers1 Mark
Question
Find the value of$i^{49}+i^{68}+i^{89}+i^{110}$
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Answer

$ i^{49}+i^{68}+i^{89}+i^{110}$
$=\left(i^4\right)^{12} \cdot i+\left(i^4\right)^{17}+\left(i^4\right)^{22} \cdot i+\left(i^4\right)^{27} \cdot i^2$
$=(1)^{12} \cdot i+(1)^{17}+(1)^{22} \cdot i+(1)^{27}(-1)$
$\quad \ldots\left[\because i^4=1, i^2=-1\right]$
$=i+1+i-1=2 i$

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