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

Sagot :

xKelvin

Answer:

See Below.

Step-by-step explanation:

We are given:

[tex]i^{4n+2}[/tex]

Using exponent properties:

[tex]=i^{4n}\cdot i^2[/tex]

Rewriting:

[tex]=(i^4)^n\cdot i^2[/tex]

Since i⁴ = 1 and i² = -1:

[tex]=(1)^n\cdot -1[/tex]

1 to any power is still 1:

[tex]=1\cdot -1 = -1[/tex]

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