Question

What is the value of 5^3i^9 -125i -15i 15i 125i

Answer 1

Answer:

$125i$

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:

$i=\sqrt{-1}$

So, elevating both members to a third power, we have:

$i^{3}=(\sqrt{-1} )^{3}=\sqrt{(-1)^{3} }=\sqrt{-1}=i$

So, $i^{3}=i$, which is the beginning, that's why we say that it's like a cycle.

So, from the problem, we have:

$5^{3} i^{9}$

To solve this, we consider the operations from the beginning:

$5^{3}=125$; and

$i^{9}=(i^{3})^{3}=(i)^{3}=i$; because $i^{3}=i$

Therefore, the result would be $125i$

Answer 2

Good morning ☕️

______

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.

:)