147/MR00. problem / Math - Solved Math Problems

MR-147. problem

Determine the value of the expression below:

$i^{225} + {(- i)}^{60} + i^{83}$

$i^{225} + {(- i)}^{60} + i^{83}$

$= i^{224} \cdot i + {(- i)}^{60} + i^{80} \cdot i^{3}$

$= i^{224} \cdot i + i^{60} + i^{80} \cdot i^{3}$

$= i^{4 \cdot 56} \cdot i + i^{4 \cdot 25} + i^{4 \cdot 20} \cdot i^{3}$

$= 1 \cdot i + 1 + 1 \cdot (- i)$

$= i + 1 - i$

$= 1$

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