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samangelzrose3576
31.12.2019 •
Mathematics
Which simplifications of the powers of i are correct?
there may be more than one correct answer. select all correct answers.
i14=i4⋅i4⋅i4⋅i2=1⋅1⋅1⋅−1=−1
i6=i4⋅i2=1⋅−1=−1
i9=i4⋅i4⋅i1=−1⋅−1⋅−i=−i
i7=i4⋅i3=1⋅i=i
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Ответ:
WRONG
CORRECT
WRONG
WRONG
Step-by-step explanation:
Some concept you might want to know:
Adding up exponent is the same thing as multiplying numbers with the same base together. So a⁴ = a²⁺² = (a²)(a²).
Another concept is that imaginary number i=√(-1). Therefore i^(even_numbers) will always give you -1. If you have i^(odd_number), leave it as a variable i and don't change it.
So if you have i^(even_number), change it to -1.
if you have i^(odd_number), keep it as i.
i¹⁴ = i⁴⁺⁴⁺⁴⁺² = (i⁴)(i⁴)(i⁴)(i²) = (-1)(-1)(-1)(-1) = 1
i⁶ = i⁴⁺² = (i⁴)(i²) = (-1)(-1) = 1
i⁹ = i⁴⁺⁴⁺¹ = (i⁴)(i⁴)(i) = (-1)(-1)(i) = i
i⁷ = i⁴⁺³= (i⁴)(i³) = (-1)(i) = -i
Ответ:
Hope this helps! (: