Question

Which of the following is equivalent to the complex number shown below?

A. 11

B. -11

C. 11i

D. -11i

Answer 1

D should be the correct answer


`i = √( - 1) \\ {i}^(2) = - 1 \\ {i}^(3) = - √( - 1) \\ {i}^(4) = 1 \\ {i}^(8) = 1 \\ {i}^(11) = {i}^(8) * {i}^(3) = 1 * - √( - 1) = - i`

Answer 2

Option D is the correct option.

Explanation:

The given expression is
`11i^(11)`

Since i = √(-1)

Therefore, i² = -1

`(i^(2))^(5)=(-1)^(5)`

`i^(10)=(-1)`

`i^(10)* i=(-1)i`

`i^(10+1)=(-i)`

`i^(11)=(-i)`

Now we multiply the expression by 11

then,
`11i^(11)=(-11i)`

Option D is the correct option.