Question

Simplify each of the following powers of i. i^15

Answer 1

Answer: $-i$

Step-by-step explanation:

You need to remember:

1. The Product of powers property: $(a^m)(a^n)=a^{(m+n)}$

2. The Power of a power property: $(a^m)^n=a^{mn}$

In this case, given:

$i^{15}$

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

1. Apply the Product of powers property:

$i^{15}=i^{12}i^2i$

2. Apply the Power of a power property:

$(i^{4})^3i^2i$

3. Finally, since $i^4=1$ and $i^2=-1$, you get:

 $=(1)(-1)(i)=-i$

Answer 2

Answer:

-i

Step-by-step explanation: