Question

Simplify i31.

Answer 1

HI!!

Answer 2

i bet this is \(i^{31}\) am i right?

Answer 3

yes:)))

Answer 4

ok her is the deal
\[i^1=i\\
i^2=-1\\
i^3=-i\\
i^4=1\] and so on

Answer 5

the pattern continues
your answer has to be one of those four \(i,-1,-i,1\)

Answer 6

take the integer remainder when you divide \(31\) by \(4\)

Answer 7

not a decimal, just the remainder
so 4 goes in to 31 7 times, with a remainder of 3 (3 left over) so \[i^{31}=i^3=-i\]

Answer 8

it has to be one of those four, like i said, and that is how you pick it

Answer 9

oh okay,i never realized thats how you figured it out!

Answer 10

not too hard when you see it right?\[i^{202}=i^2=-1\] for example

Answer 11

not at all! thank you :)

Answer 12

\[\color\magenta\heartsuit\]