Question

Which of the following imaginary numbers is simplified INCORRECTLY?
Answer
A. i42 = -1
B. i17 = i
C. i56 = -1
D. i43 = -i

Answer 1

Do you mean i^n. Hmm I came out with a general formula.

To justify between -1 and 1, you may use this formula:
\[i^{2n}\]
if n=1,3,5,7,..., then the answer would be -1.
if n=2,4,6,8,...,then the answer would be 1.

To justify between i or -i, use this formula:
\[i^{2n-1}\]
if n=1,3,5,7,....,then the answer would be i.
if n=2,4,6,8,...,then the answer would be -i.

as an example, we take the 1st choice. they want us to justtify whether i^42 is equal to -1. since -1 is involved, we choose the formula \[i^{2n}\]
so just let 2n=42, we get n=21 which belongs to the situation n=1,3,5,... therefore the answer for i^42 is 1, which is correct.

use this concept and you will be able to judege which is incorrect.

Answer 2

the answer for 1st choice should be -1. typo. For choice B, we need to justify whether i^17 is equal to i. since i is involved we use the formula i^(2n-1).

so just let 2n-1=17, we get n=9 whereby n belongs to n=1,3,5,9,.. this group therefore we can conclude that i is the answer for i^17.

Answer 3

None of the given choice is correct. The reason being that none of the imaginary numbers given can be simplified.