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

1 Answer
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#.