They are garbling the heck out of this.........they do not like me posting this type of stuff....

More powers of $i$i

Let's keep this going! Let's find the next $4$4 powers of $i$i using a similar method.

i5=i4⋅i     =1⋅i=iProperties of exponentsSince i4=1

i6=i4⋅i2=1⋅(−1)=−1Properties of exponentsSince i4=1 and i2=−1

i7=i4⋅i3=1⋅(−i)=−iProperties of exponentsSince i4=1 and i3=−i

i8=i4⋅i4    =1⋅1=1Properties of exponentsSince i4=1 

The results are summarized in the table