Simplifying Powers of i
In this lesson, we learn how to simplify powers of i by expressing them as either a power of i, negative i, one, or negative one. Since i has four options (i, -1, -i, 1), we can divide the exponent by four to determine the remainder and simplify the power accordingly. If the remainder is zero, the power is one, and if the remainder is one, the power is i, and so on. This method simplifies the process and allows us to quickly determine the value of any power of i.
Simplifying imaginary numbers
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- Simplify i^42, i^56
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Staff Review
I think it would be easier if i^40 is expressed as (i^4)^10=>1^10=>1 i^25 as (i^4)^6.i=>1.i=>i i^50 as (i^4)^12.i²=>1.(-1)=>-1
