Question

Find the value of
$i+i^{2}+i^{3}+i^{4}$

Answer 1

We know that

${i}^{2} = - 1 \\ \\ {i}^{4} = 1$
$i+i^{2}+i^{3}+i^{4} \\ \\ = i - 1 + {i}^{2} i + 1 \\ \\ = i - 1 + ( - 1)i + 1 \\ \\ i - 1 - i + 1 \\ \\ = 0$
So
$i+i^{2}+i^{3}+i^{4}=0$

Hope it helps you.