Find the value of : i^ 49 +i^ 68 +i^ 89 +i^ 110 - Vidyadip

Question

Find the value of : $i^{49}+i^{68}+i^{89}+i^{110}$

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Answer

$\begin{aligned} & i^{49}+i^{68}+i^{89}+i^{110} \\ & =\left(i^4\right)^{12} \cdot i+\left(i^4\right)^{17}+\left(i^4\right)^{22} \cdot i+\left(i^4\right)^{27} \cdot i^2 \\ & \left.=(1)^{12} \cdot i+(1)^{17}+(1)^{22} \cdot i+(1)^{27}(-1) \ldots \ldots . . \because i^4=1, i^2=-1\right] \\ & =\mathrm{i}+1+\mathrm{i}-1 \\ & =2 \mathrm{i} \\ & \end{aligned}$

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