Question

Which expression is equivalent to i 233

Answer 1

Answer:C

Explanation:

Answer 2

Start with second, third and fourth degree of imaginary unit i:


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

Since 233=232+1=4·58+1, then
`i^(233)=i^(4\cdot 58+1)=(i^4)^(58)\cdot i^1=1^(58)\cdot i=i`.

Answer:
`i^(233)=i`