Question

Helpppppppppppppppppppppppppp

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.