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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers1 Mark
Question
Simplify
$\left(i^{65}+\frac{1}{i^{145}}\right)$
✓

Answer

$\left(i^{65}+\frac{1}{i^{145}}\right)$
$=\left[\left(i^4\right)^{16} \cdot i+\frac{1}{\left(i^4\right)^{36} \cdot i}\right]=i+\frac{1}{i}=\frac{i^2+1}{i}$
$=\frac{-1+1}{i}$
$=0$

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