Question

Why does the expression i to the power 4n+2 is always equal to -1​

Answer 1

See Below.

Explanation:

We are given:

`i^(4n+2)`

Using exponent properties:

`=i^(4n)\cdot i^2`

Rewriting:

`=(i^4)^n\cdot i^2`

Since i⁴ = 1 and i² = -1:

`=(1)^n\cdot -1`

1 to any power is still 1:

`=1\cdot -1 = -1`