Posted by **yengiang** on Saturday, October 27, 2012 at 2:39pm.

Simplify: (1-i)^3

Here's how I break it down using the formula (x-y)^3 but I just don't know how to get to the final answer. Please help.

= 1-3i+3(i)^2-(i)^3

Thank you

- Math - 10th grade -
**Steve**, Saturday, October 27, 2012 at 2:46pm
so far, so good. Remember that

i^2 = -1

i^3 = -i

and you have

1 - 3i - 3 + i

-2 - 2i

- Math - 10th grade -
**Reiny**, Saturday, October 27, 2012 at 2:47pm
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

- Math - 10th grade -
**yengiang**, Saturday, October 27, 2012 at 3:18pm
Please explain why i^2=-1

- Math - 10th grade -
**Reiny**, Saturday, October 27, 2012 at 3:23pm
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

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