Question

Evaluate i^31 please help

Answer 1

ANSWER

${i}^{31} = - i$

EXPLANATION

We want to evaluate

${i}^{31}$

Use indices to rewrite the expression as:

$= {i}^{30} \times i$

We know that

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

So we rewrite the expression to obtain;

$= ({ {i}^{2}) }^{15} \times i$

This gives us;

$= {( - 1) }^{15} \times i$

This simplifies to

$= - 1 \times i$

$= - i$