SOLUTION: i am unsure of how to cube a simple complex number, please help! : {{{ (1-i)^3 }}}

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Question 160204: i am unsure of how to cube a simple complex number, please help! : +%281-i%29%5E3+
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
+%281-i%29%5E3+

Write it down three times as a factor:

+%281-i%29%281-i%29%281-i%29+

Use FOIL on the first and second factors, leaving the
third alone for the moment:


+%281-i-i%2Bi%5E2%29%281-i%29+

Now combine the -i-i as -2i

%281-2i%2Bi%5E2%29%281-i%29+

Now replace the i%5E2 by -1

%281-2i%2B%28-1%29%29%281-i%29+

+%281-2i-1%29%281-i%29+

The 1 and the -1 cancel out:

+%28-2i%29%281-i%29+

Distribute:

-2i%2B2i%5E2

Now replace the i%5E2 by -1

-2i%2B2%28-1%29

-2i-2

Write in standard order:

-2-2i

Edwin