SOLUTION: If {{{i^(x+2)+i^(x)+i^(x-2)=1}}}, then what is the value of x? (Note: {{{i=sqrt(-1)}}} ) A)0 B)1 C)2 D)3

Algebra ->  Expressions -> SOLUTION: If {{{i^(x+2)+i^(x)+i^(x-2)=1}}}, then what is the value of x? (Note: {{{i=sqrt(-1)}}} ) A)0 B)1 C)2 D)3       Log On


   

Question 1042048: If i%5E%28x%2B2%29%2Bi%5E%28x%29%2Bi%5E%28x-2%29=1, then what is the value of x? (Note: i=sqrt%28-1%29 )
A)0
B)1
C)2
D)3
Found 3 solutions by Alan3354, ikleyn, solver91311:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
With only 4 to choose from, try each one.
See which works.

Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.
If i%5E%28x%2B2%29%2Bi%5E%28x%29%2Bi%5E%28x-2%29=1, then what is the value of x? (Note: i=sqrt%28-1%29 )
A)0
B)1
C)2
D)3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

For any (integer) x,  i%5E%28x%2B2%29+%2B+i%5Ex = 0,  since i%5E%28x%2B2%29  and  i%5Ex have opposite signs  (due to   i%5E2 = -1).


So, it leaves i%5E%28x-2%29 = 1,  which implies  x-2 = 0, or 4, or 8, . . . and so on.  From the given options,  x = 2  works (option C).


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Use the following facts, then evaluate your function with each of the choices. One of them works.















John

My calculator said it, I believe it, that settles it