# Write the complex number i^17 in standard form?

May 22, 2015

With $i$, it's important to know how its exponents cycle:

$i = i$
${i}^{2} = - 1$
${i}^{3} = - i$
${i}^{4} = 1$
${i}^{5} = i$
and so on.

Every 4 exponents, the cycle repeats. For every multiple of 4 (let's call it 'n'), ${i}^{n}$ = 1.

${i}^{17}$ = ${i}^{16} \times i$ = $1 \times i$ = $i$

So, ${i}^{17}$ is just $i$.