Question 256096
<pre><font size = 4 color = "indigo"><b>
{{{ (1/2 + (sqrt(3)/2)  i )^2 }}}

{{{ (1/2 + (sqrt(3)/2)  i )(1/2 + (sqrt(3)/2)  i )}}}

Use "FOIL":

{{{(1/2)^2 + (1/2)(sqrt(3)/2)i + (1/2)(sqrt(3)/2)i + ((sqrt(3)/2)i)^2}}}

{{{1/4 + (sqrt(3)/4)i + (sqrt(3)/4)i + (3/4)i^2}}}

Combine the middle terms and replace {{{i^2}}} by {{{-1}}}

{{{1/4 + (2sqrt(3)/4)i + (3/4)(-1)}}}

Simplify

{{{1/4 + (sqrt(3)/2)i -3/4}}}

{{{-2/4 + (sqrt(3)/2)i}}}


{{{-1/2 + (sqrt(3)/2)i}}}

Edwin</pre>