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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers1 Mark
Question
Evaluate the following:$i^{30}+i^{40}+i^{50}+i^{60}$
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Answer

We know that, $i^2=-1, i^3=-i, i^4=1$
$ i^{30}+i^{40}+i^{50}+i^{60}$
$=\left(i^4\right)^7 i^2+\left(i^4\right)^{10}+\left(i^4\right)^{12} i^2+\left(i^4\right)^{15}$
$=(1)^7(-1)+(1)^{10}+(1)^{12}(-1)+(1)^{15}$
$=-1+1-1+1=0$

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