Question 599389


{{{(6+5i)^2}}} Start with the given expression.



{{{(6+5i)(6+5i)}}} 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(6)+5i)(highlight(6)+5i)}}} Multiply the <font color="red">F</font>irst terms:{{{(6)*(6)=36}}}.



{{{(highlight(6)+5i)(6+highlight(5i))}}} Multiply the <font color="red">O</font>uter terms:{{{(6)*(5*i)=30*i}}}.



{{{(6+highlight(5i))(highlight(6)+5i)}}} Multiply the <font color="red">I</font>nner terms:{{{(5*i)*(6)=30*i}}}.



{{{(6+highlight(5i))(6+highlight(5i))}}} Multiply the <font color="red">L</font>ast terms:{{{(5i)*(5i) = 25i^2=25(-1)=-25}}}.



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So we have the terms: {{{36}}}, {{{30*i}}}, {{{30*i}}}, {{{-25}}} 



{{{36+30*i+30*i-25}}} Now add every term listed above to make a single expression.



{{{11+60i}}} Now combine like terms.



So {{{(6+5i)^2}}} FOILs to {{{11+60i}}}.



In other words, {{{(6+5i)^2=11+60i}}}.