Respuesta :

luisejr77

Answer: [tex]-i[/tex]

Step-by-step explanation:

You need to remember:

1. The Product of powers property: [tex](a^m)(a^n)=a^{(m+n)}[/tex]

2. The Power of a power property: [tex](a^m)^n=a^{mn}[/tex]

In this case, given:

[tex]i^{15}[/tex]

You need to follow these steps in order to simplify it:

1. Apply the Product of powers property:

[tex]i^{15}=i^{12}i^2i[/tex]

2. Apply the Power of a power property:

[tex](i^{4})^3i^2i[/tex]

3. Finally, since [tex]i^4=1[/tex] and [tex]i^2=-1[/tex], you get:

 [tex]=(1)(-1)(i)=-i[/tex]

abidemiokin

The simplified form of the complex power [tex]i^{15}[/tex] is [tex]-i[/tex]

The square root of any negative number leads to a complex number. For example:

[tex]\sqrt{-1}=i\\i^2=-1[/tex]

Given the complex expression, [tex]i^{15}[/tex]. This can be expressed as:

[tex]i^{15}\\=i^{14} \times i\\=(i^2)^7 \times i\\[/tex]

Substitute i² = -1 into the result to have:

[tex]= (-1)^7 \times i\\= -1 \times i\\= -i[/tex]

This shows that the value of the complex power [tex]i^{15}[/tex] is [tex]-i[/tex]

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