Question

For the imaginary unit, I and integer x, which of the following is not a possible value of i^x?o i o 2io -1o 1

Answer 1

`\begin{gathered} i^x \\ \\ \text{Properties:} \\ i^2=-1 \\ i^3=i^2\cdot i=-1i=-i \\ i^4=i^2\cdot i^2=(-1)(-1)=1^{} \\ i^5=i^4\cdot i=1\cdot i=i \\ i^6=i^4\cdot i^2=1\cdot(-1)=-1 \\ i^7=i^6\cdot i=-1i=-i \\ i^8=i^4\cdot i^4=1\cdot1=1 \\ \\ \end{gathered}`

As you can see above the imaginary unit powered to al whole number always follows the sequence: i, -1, -i, 1, i, -1, -i,1....

Then, for the given options the 2i is not a possible value for i powered to a whole number.Answer: 2i