Question

What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?

Answer 1

The problem is: What is the value of the expression



`\displaystyle{ i^0\cdot i^1\cdot i^2\cdot i^3\cdot i^4`.

We know that
`i^0=1` and
`i^2=-1`. Thus:


`i^0=1\\\\i^1=i\\\\i^2=-1\\\\i^3=i^2\cdot i=-1 \cdot i=-i\\\\i^4=(i^2)^2=(-1)^2=1.`

So,


`i^0\cdot i^1\cdot i^2\cdot i^3\cdot i^4=1 \cdot i \cdot (-1) \cdot (-i) \cdot 1= i \cdot (-1) \cdot (-i)= i \cdot i=-1.`


Answer: B) -1.