Question 195737


{{{(z-i)^2}}} Start with the given expression.



{{{(1/6-i)(1/6-i)}}} Expand. Remember something like {{{x^2=x*x}}}.



Now let's FOIL the expression.



Remember, when you FOIL an expression, you follow this procedure:



{{{(highlight(1/6)-i)(highlight(1/6)-i)}}} Multiply the <font color="red">F</font>irst terms:{{{(1/6)*(1/6)=(1/6)^2=1/36}}}.



{{{(highlight(1/6)-i)(z+highlight(-i))}}} Multiply the <font color="red">O</font>uter terms:{{{(1/6)*(-i)=-(1/6)*i}}}.



{{{(1/6+highlight(-i))(highlight(1/6)-i)}}} Multiply the <font color="red">I</font>nner terms:{{{(-i)*(1/6)=-(1/6)*i}}}.



{{{(1/6+highlight(-i))(1/6+highlight(-i))}}} Multiply the <font color="red">L</font>ast terms:{{{(-i)*(-i)=i^2=-1}}}.



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So we have the terms: {{{1/36}}}, {{{-(1/6)*i}}}, {{{-(1/6)*i}}}, and {{{-1}}} 



{{{1/36-(1/6)*i-(1/6)*i-1}}} Now add every term listed above to make a single expression.



{{{-35/36-(1/3)i}}} Now combine like terms.



So {{{(1/6-i)^2}}} FOILs to {{{-35/36-(1/3)i}}}.



In other words, {{{(1/6-i)^2=-35/36-(1/3)i}}}.