Final answer:
When raised to the power of 79, i simplifies to -i due to the cyclical nature of its powers.
Step-by-step explanation:
To understand why i raised to the power of 79 is equal to -i, we need to know how the powers of i cycle. The powers of i follow a repeating pattern:
i1 = i, i2 = -1, i3 = -i, i4 = 1, i5 = i, i6 = -1, and so on.
Since 79 is one less than a multiple of 4 (79 = 19 x 4 + 3), the power of i can be simplified:
i79 = i4 x 19 + 3 = (i4)19 x i3 = 119 x (-i) = -i
So therefore when we raise i, the imaginary unit, to the power 79, we get -i as the result. This can be explained by using the properties of complex numbers.