Question

which of the following is equivalent to i⁹A. i²⁷/i³B. (i⁴) (i⁵)C. (i³)²D. iE. (i • i) x (i•i•i•i) x (i•i•i) F. (i³)³(there could be more than one answer)

Answer 1

`i^9=i^(1+4+4)=i\cdot i^4\cdot i^4=i\cdot1\cdot1=i`
`(i^(27))/(i^3)=i^(27-3)=i^(24)=i^(4\cdot6)=(i^4)^6=1^6=1`
`i^4\cdot i^5=i^(4+5)=i^9=i`
`(i^3)^2=i^(3\cdot2)=i^6=i^(4+2)=i^4\cdot i^2=1\cdot(-1)=-1`
`(i\cdot i)\cdot(i\cdot i\cdot i\cdot i)\cdot(i\cdot i\cdot i)=i^2\cdot i^4\cdot i^3=i^(2+4+3)=i^9=i`
`(i^3)^3=i^(3\cdot3)=i^9=i`

Options B, D, E, and F are correct