Question

Simplify.
Find the number of powers with a multiple of 4 first.

Answer 1

The boxes are filled with ...

• 2
• 2
• -1

Explanation:

You want to simplify the expression i¹⁰ by writing it in terms of i⁴ and another power of i.

Simplify

10 can be expressed as a multiple of 4 like this:

10 = 4·2 +2

This means we can write ...

`\displaystyle i^(10)=\boxed{(i^4)^2\,i^2}`

Powers of i

We know that i² = -1, so ...

i⁴ = (i²)² = (-1)² = 1

Then the product is ...

`i^(10)=(i^4)^2\,i^2\\\\i^(10)=(1)^2\,(-1)\\\\\boxed{i^(10)=-1}`

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