Academic Subjects
Math
Algebra
Sequences & Series
Sequence Of i

What is the sequence of i?



The i stands for 'imaginary number'...
a rather unfortunate name, yes

Let's write out our sequence
we know that i2 = -1,
so let's built on that



imaginary numbers

i0 = 1
i1 = i
i2 = -1
i3 = (i1)(i2) = (i)(-1) = -i
i4 = (i2)(i2) = (-1)(-1) = 1
i5 = (i2)(i3) = (-1)(-i) = i
i6 = (i2)(i4) = (-1)(1) = -1
i7 = (i3)(i4) = (-i)(1) = -i
i8 = (i4)(i4) = (1)(1) = 1
i9 = (i4)(i5) = (1)(i) = i
i10 = (i5)(i5) = (i)(i) = i2 = -1
i11 = (i5)(i6) = (i)(-1) = -i

see the pattern...