Question

Which of the following is equivalent to the

complex number ;³¹?
Choose 1 answer:
A
B
C
D
1
i
-1
-i

Answer 1

Explanation:

`= {i}^(31)`

`= {i}^(28) * {i}^(3)`

`= {( {i}^(4) )}^(7) * ( {i}^(2) * i)`

`= ( {i}^(2) * {i}^(2) ) {}^(7) * {i}^(2) * i`

`= ( - 1 * ( - 1)) {}^(7) * ( - 1) * i`

`= {1}^(7) * ( - i)`

`= 1 * ( - i)`

`= - i`

The answer is D.