$i^{2} + i^{3} + i^{4} + i^{3}$ is equal to

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Solution

We know that $i^{2} = - 1$

$i^{2} + i^{3} + i^{4} + i^{3}$ $= i^{2} + i^{2} \times i + i^{2} \times i^{2} + i^{2} \times i$

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

$= - 1 - i + 1 - i$

$i^{2} + i^{3} + i^{4} + i^{3} = - 2 i$

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