i the Imaginary Number

i = imaginary unit

The letter i, when use to represent a number is known as “the imaginary number”.

Given the definition of i both of the following statements are true:
i^2 = -1 and i =  {sqrt{-i}}

i^0 = 1
Any number with an exponent of 0 is equal to 1.

i^1 = i

i^2 = -1

i^3 = -i
Solution:
i^3 = i^2 * i
if:
 i^2 = -1
then
i^3 = -1 * i = -i

i^4 = 1
Solution:
i^4 = i * i^3
if
 i^3 = -i
then
i * -i
is also
-1(i)(i)
multiplication is commutative
therefore:
-1(i)(i) = -1(i^2) = (-1)(-1) = 1

i^5 = i
Solution:
i^5 = i^4 x i
if
i^4 = 1
then
i5 = 1 * i = i

The pattern of -1, -i, 1, i is repeated, infinitely.

i^6 = -1
i^7 = -i
i^8 = 1
i^9 = i.

i^10 = -1
i^11 = -i
i^12 = 1
i^13 = i

i^14 = -1
i^15 = -i
i^16 = 1
i^17 = i


 

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