Question

$i + {i}^{2} + {i}^{3} + {i}^{4}$
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Answer 1

HEY MATE HERE IS YOUR ANSWER:

•Use Square Rule:

${i}^{2} = - 1$

1:

$i - 1 + {i}^{3} + {i}^{4}$

•Isolate:

${i}^{2}$

2:

$i - 1 + {i}^{2} i + {i}^{4}$

•Use Square Rule:

${i}^{2} = - 1$

3:

$i - 1 - 1 \times i + {i}^{4}$

•Use fourth power rule:

${i}^{4} = {i}^{2} {i}^{2} = ( - 1)( - 1) = 1$

4:

$i - 1 - 1 \times i + 1$

•Simplify;

$1 \times i \: to \: i$

5:

$i - 1 - i + 1$

•Collect like terms:

6:

$( - 1 + 1) + (i - i)$

•Simplify:

Answer:

$0$