Question 168737


{{{(2+3i)(1-5i)}}} Start with the given expression.



Now let's FOIL the expression.



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



{{{(highlight(2)+3i)(highlight(1)-5i)}}} Multiply the <font color="red">F</font>irst terms:{{{(2)*(1)=2}}}.



{{{(highlight(2)+3i)(1+highlight(-5i))}}} Multiply the <font color="red">O</font>uter terms:{{{(2)*(-5i)=-10i}}}.



{{{(2+highlight(3i))(highlight(1)-5i)}}} Multiply the <font color="red">I</font>nner terms:{{{(3i)*(1)=3i}}}.



{{{(2+highlight(3i))(1+highlight(-5i))}}} Multiply the <font color="red">L</font>ast terms:{{{(3*i)*(-5*i)=-15i^2}}}.



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{{{2-10i+3i-15i^2}}} Now collect every term to make a single expression.



{{{2-7i-15i^2}}} Now combine like terms.



{{{2-7i-15(-1)}}} Replace {{{i^2}}} with -1 (note: I'm assuming that you are dealing with imaginary numbers, so remember that {{{i^2=-1}}} )



{{{2-7i+15}}} Multiply



{{{17-7i}}} Combine like terms.



So {{{(2+3i)(1-5i)}}} FOILs and simplifies to {{{17-7i}}}.



In other words, {{{(2+3i)(1-5i)=17-7i}}}.