SOLUTION: What is {{{ i^13 }}} simflied? A.) {{{ 1 }}} B.) {{{ -1 }}} C.) {{{ i }}} D.) {{{-i }}} Thanks

Algebra ->  Finance -> SOLUTION: What is {{{ i^13 }}} simflied? A.) {{{ 1 }}} B.) {{{ -1 }}} C.) {{{ i }}} D.) {{{-i }}} Thanks      Log On


   

Question 1030811: What is +i%5E13+ simflied?
A.) +1+
B.) +-1+
C.) +i+
D.) -i+
Thanks
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Option C). 

i%5E2 = -1,

i%5E3 = i%5E2%2Ai = %28-1%29%2Ai = -i,

i%5E4 = i%5E2%2Ai%5E2 = %28-1%29%2A%28-1%29 = 1,

i%5E5 = i%5E4%5Ei = i,  

and so on, with the cyclic period of 4.

Therefore, i%5E13 = i%5E12%2Ai = i.