Math  10th grade
posted by yengiang .
Simplify: (1i)^3
Here's how I break it down using the formula (xy)^3 but I just don't know how to get to the final answer. Please help.
= 13i+3(i)^2(i)^3
Thank you

so far, so good. Remember that
i^2 = 1
i^3 = i
and you have
1  3i  3 + i
2  2i 
your expansion is correct, except now you have to reduce the powers of i
look at this pattern
i^1 = i
i^2 = 1
i^3 = (i^2)i = i
i^4 = (i^2)(i^2) = (1)(1) = 1
i^5 = (i^4)(i) = i
so it runs:
i , 1 , i , +1 , i , 1 , i , +1 , .....
notice that if the exponent is divisble by 4 i^n  = +1
if the exponent is even but not divisible by 4 i^n = 1
back to yours ...
1  3i + 3i^2  i^3
= 1  3i  3 + i
= 2  2i 
Please explain why i^2=1

by definition:
i = √1
square both sides
i^2 = (√1)(√1) = 1
when you multiply √x by √x you get x
e.g. √48√48 = 48
√12.698√12.698 = 12.698