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

Question

asked Apr 21, 2022 14.5k views

1 Answer

CharlieB · Answer 1 · 2022-04-27T14:21:04+0000

Answer:

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:

$=1\cdot -1 = -1$