Question

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Answer 1

To multiply the imaginary number i, we still can use the product rule for exponents. When we multiply, we get $i^{0+1+2+3+4}=i^{10}$.

Now, simplifying this might seem formidable at first. But, let's start working through different powers of i.

$i^0=1\\i^1=i\\i^2=-1\\i^3=-i\\i^4=(-1)(-1)=1$

Notice that $i^4=1$. That means that any power that is a multiply of four will also be 1. For instance, $i^8=1,\ i^{12}=1$, and so on... 

If we rewrite $i^{10}$ with this in mind, we can break it down into smaller pieces and simplify. 

$i^{10}=i^{4+4+2}=(i^4)(i^4)(i^2)=(1)(1)(-1)=-1$

The answer is B.