Question 762782: how to solve i^15 step by step
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! i^15
i^(12+3)
i^(12)*i^3
(i^(3*4))*i^3
(i^3)^4*i^3
(-i)^4*(-i)
(-1)^4*(i)^4*(-i)
(-1)^4*(i^2)^2*(-i)
(-1)^4*(-1)^2*(-i)
(-1)^4*1*(-i)
(-1)^4*(-i)
1*(-i)
-i
So i^15 = -i
Shortcut: divide 15 by 4 to get 3 remainder 3. The remainder of 3 means that i^(15) = i^3. Since i^3 = -i, this means i^15 = -i
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