SOLUTION: i^5(i^2-3i) My book says the answer is 3-i but I cannot get to that answer. Can you show me how

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: i^5(i^2-3i) My book says the answer is 3-i but I cannot get to that answer. Can you show me how      Log On


   

Question 842017: i^5(i^2-3i)
My book says the answer is 3-i but I cannot get to that answer.
Can you show me how
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
First try distributive property:
i%5E5%2Ai%5E2-3i%2Ai%5E5
i%5E7-3i%5E6
-
From here, pay careful attention to the whole number powers of i.
You already know i^2=-1; and you understand that %28-1%29%28-1%29=i%5E2%2Ai%5E2=1 or i%5E4=1.
Showing the first few powers of i:
i%5E0=what
i%5E1=i
i%5E2=-1
i%5E3=-i------ (think how this makes sense.)
i%5E4=1
i%5E5=i%2Ai%5E4=i
i%5E6=i%2Ai%5E5=-1
i%5E7=-i
.
The pattern should tell you also that i%5E0=1.
Also notice how the values cycle. They go in a cycle of i, -1, -i, 1; and this cycle repeats.

Back to the unfinished expression from your given one,
i%5E7-3i%5E6
-i-3%28-1%29
highlight%28-i%2B3%29 or highlight%283-i%29.