Question

find the value of i7​

Answer 1

Answer:

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 i i1 i2 i3 i4 i5 i6 i7 i8 i9

Simplified i -1 -i 1 i -1 -i 1 i

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.

For example, when the exponent is 55

55/4= 13 remainder 3

We now know that i55=(i4)13×i3=1×i3=-1

Step-by-step explanation:

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