Question 160204
{{{ (1-i)^3 }}}
<pre><font size = 4 color = "indigo"><b>
Write it down three times as a factor:

{{{ (1-i)(1-i)(1-i) }}}

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


{{{ (1-i-i+i^2)(1-i) }}}

Now combine the {{{-i-i}}} as {{{-2i}}}

{{{(1-2i+i^2)(1-i) }}}

Now replace the {{{i^2}}} by {{{-1}}}

{{{(1-2i+(-1))(1-i) }}}

{{{ (1-2i-1)(1-i) }}}

The 1 and the -1 cancel out:

{{{ (-2i)(1-i) }}}

Distribute:

{{{-2i+2i^2}}}

Now replace the {{{i^2}}} by {{{-1}}}

{{{-2i+2(-1)}}}

{{{-2i-2}}}

Write in standard order:

{{{-2-2i}}}

Edwin</pre>