document.write( "Question 400985: (2-3i)-(4-5i)+(-3+2i) \n" ); document.write( "
Algebra.Com's Answer #283781 by jsmallt9(3758)\"\" \"About 
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(2-3i) - (4-5i) + (-3+2i)
\n" ); document.write( "For many reasons it is a good idea to change any subtractions to additions of the opposite:
  • Addition is easier than subtraction.
  • Addition is Commutative so the order can be changed in any desired way.
  • Addition is Associative so the grouping can be changed in any desired way.
  • Most \"forms\" are written in terms of addition:
    • Slope-intercept form (of the equation of a line): y = mx + b
    • Standard form (of the euqation of a line): Ax + By = C
    • Complex numbers: a + bi
    • Quadratic equations: \"ax%5E2+%2B+bx+%2B+c+=+0\"
    • etc.

\n" ); document.write( "Rewriting the subtractions as additions of the opposite we get:
\n" ); document.write( "(2+(-3i)) - (4+(-5i)) + (-3+2i)
\n" ); document.write( "(2+(-3i)) + (-4+5i)) + (-3+2i)
\n" ); document.write( "Only like terms can be added. So we will rearrange the order and the grouping so that all the like terms are grouped:
\n" ); document.write( "(2+(-4)+(-3)) + (-3i+5i+2i)
\n" ); document.write( "Adding we get:
\n" ); document.write( "-5 + 4i
\n" ); document.write( "And we are finished. \n" ); document.write( "
\n" );