Question

If "i" is raised to an odd power, then it cannot simplify to be
a)-1
b)-i
c)i

Answer 1

Hence, option A is correct.

Explanation:

'i' is a complex number with the property that:

`i^2=-1\\\\i^3=-i\\\\i^4=1\\\\i^5=i`

and the terms will continue so on.

if i is raised to an odd power then we will never get '-1' term.

Because every even power of i will be either '1' or '-1' and so the next power of the even power will be odd and hence '1' or '-1' will get multiplied by i and hence lead to the term either 'i' or '-i'.

Hence If "i" is raised to an odd power, then it cannot simplify to be '-1'.

Hence, option A is correct.

Answer 2

i ^1 = i
i ^ 2 = - 1
i ^ 3 = - i
i ^4 = 1
etc.
................
"i" raised to an odd power cannot simplify to be : A ) - 1