To multiply the imaginary number i, we still can use the product rule for exponents. When we multiply, we get [tex]i^{0+1+2+3+4}=i^{10}[/tex].
Now, simplifying this might seem formidable at first. But, let's start working through different powers of i.
[tex]i^0=1\\i^1=i\\i^2=-1\\i^3=-i\\i^4=(-1)(-1)=1[/tex]
Notice that [tex]i^4=1[/tex]. That means that any power that is a multiply of four will also be 1. For instance, [tex]i^8=1,\ i^{12}=1[/tex], and so on...
If we rewrite [tex]i^{10}[/tex] with this in mind, we can break it down into smaller pieces and simplify.
[tex]i^{10}=i^{4+4+2}=(i^4)(i^4)(i^2)=(1)(1)(-1)=-1[/tex]
The answer is B.
