Equivalent to the complex number i^14

The powers of i have a repetitive cyclic nature.

When we raise the imagenry unit i to increasing powers, we get a pattern which repeats itself.

Observe the following table of powers of i.

Power of ii1i2i3i4i5i6i7i8i9

Simplifiedi-1-i1i-1-i1i

As you see above, the pattern repeats itself and is four members long.

Therefore, ix+8 ix+4 will equalx.

When asked to determine the value of i to a power higher than 4, we can use this information in order to find our position in the cycle.

So, instead of using the actual power, we can take the remainder of the power divided by 4.

step-by-step explanation: