Respuesta :
Good morning ☕️
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Answer:
125i
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Step-by-step explanation:
5³× i⁹ = 125 × i¹ = 125i
By the way :
i⁹ = (i⁴)²× i¹ = (1)²×i = i.
:)
Answer:
[tex]125i[/tex]
Step-by-step explanation:
When we have potential expression that include imaginary numbers, we have to consider some basic results, because these imaginary potential expression are cyclical.
We know that:
[tex]i=\sqrt{-1}[/tex]
So, elevating both members to a third power, we have:
[tex]i^{3}=(\sqrt{-1} )^{3}=\sqrt{(-1)^{3} }=\sqrt{-1}=i[/tex]
So, [tex]i^{3}=i[/tex], which is the beginning, that's why we say that it's like a cycle.
So, from the problem, we have:
[tex]5^{3} i^{9}[/tex]
To solve this, we consider the operations from the beginning:
[tex]5^{3}=125[/tex]; and
[tex]i^{9}=(i^{3})^{3}=(i)^{3}=i[/tex]; because [tex]i^{3}=i[/tex]
Therefore, the result would be [tex]125i[/tex]
