Question 148307

{{{(3-2i)^2}}} Start with the given expression.



{{{(3-2i)(3-2i)}}} 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(3)-2i)(highlight(3)-2i)}}} Multiply the <font color="red">F</font>irst terms:{{{(3)*(3)=9}}}.



{{{(highlight(3)-2i)(3+highlight(-2i))}}} Multiply the <font color="red">O</font>uter terms:{{{(3)*(-2*i)=-6*i}}}.



{{{(3+highlight(-2i))(highlight(3)-2i)}}} Multiply the <font color="red">I</font>nner terms:{{{(-2*i)*(3)=-6*i}}}.



{{{(3+highlight(-2i))(3+highlight(-2i))}}} Multiply the <font color="red">L</font>ast terms:{{{(-2*i)*(-2*i)=4*i^2=4(-1)=-4}}}.



{{{9-6*i-6*i-4}}} Now collect every term to make a single expression.



{{{5-12*i}}} Now combine like terms.



Now the number is in standard form a+bi where a=5 and b=-12