Question

Simplify i^72

i
-1
-i
1

Answer 1

@jim_thompson5910

Answer 2

same idea as before

Answer 3

the pattern is
\[i^1=i\\
i^2=-1\\
i^3=-i\\
i^4=1\] etc

Answer 4

so do you divide 72 by 4 again..

Answer 5

take the integer remainder when you divide \(72\) by \(4\)
since \(4\) goes in to \(72\) evenly there is no remainder
that makes
\[i^{72}=i^0=1\]

Answer 6

yeah same process every time

Answer 7

ok

Answer 8

thank youu!!

Answer 9

\[i^{105}=i^1=i\] for example

Answer 10

yw

Answer 11

Going the long route

\[\Large i^{72} = i^{4*18}\]

\[\Large i^{72} = (i^{4})^{18}\]

\[\Large i^{72} = (1)^{18}\]

\[\Large i^{72} = 1\]

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Or the short way,

72/4 = 18 remainder 0

So that means

\[\Large i^{72} = i^{0}\]

notice how the remainder of 0 is present in the exponent, so,

\[\Large i^{72} = i^{0}\]

\[\Large i^{72} = 1\]

which is a nice shortcut