Question

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

Answer 1

Answer:

See Below.

Step-by-step 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:

$=1\cdot -1 = -1$