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Math Help - Complex Numbers-basic operations

  1. #1
    Member Awsom Guy's Avatar
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    Complex Numbers-basic operations

    I think this goes in this section but anyway...

    Simplify..
    -3-i/1+i + 1+3i/1-i
    I hope this makes sense.
    The answer is -3+3i
    This is my working but I can't get the answer..
    -3-i/1+i * 1-i/1-i
    (-3-i)(1-i)
    -3(1-i)-i(1-i)
    -3+3i-i-1
    -4+2i
    Then....
    1+3i/1-i * 1+i/1+i
    (1+3i)(1+i)
    (1+3i)(1+i)
    1(1+i)+3i(1+i)
    1+i+3i-3
    -2+4i
    Finally..
    -4+2i-2+4i
    -6+6i

    This is my working but I cannot get the right answer....
    Thanks
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  2. #2
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    You left out the denominator in your work
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  3. #3
    Member Awsom Guy's Avatar
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    No change

    well I didn't put it in because it is a one and it doesn't change anything....
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  4. #4
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    It's 2
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  5. #5
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    Quote Originally Posted by Awsom Guy View Post
    I think this goes in this section but anyway...

    Simplify..
    -3-i/1+i + 1+3i/1-i
    I hope this makes sense.
    No, it doesn't because you have left out parentheses. Do you mean
    (-3-i)/(1+i)+ (1+3)/(1-i)?

    The answer is -3+3i
    This is my working but I can't get the answer..
    -3-i/1+i * 1-i/1-i
    (-3-i)(1-i)
    -3(1-i)-i(1-i)
    -3+3i-i-1
    -4+2i
    Then....
    1+3i/1-i * 1+i/1+i
    (1+3i)(1+i)
    (1+3i)(1+i)
    1(1+i)+3i(1+i)
    1+i+3i-3
    -2+4i
    Finally..
    -4+2i-2+4i
    -6+6i

    This is my working but I cannot get the right answer....
    Thanks
    You've written things in a very confused way!

    Simplify (-3-i)/(1+i) by 'rationalizing' the denominator: (-3-i)(1-i)/(1+i)(1-i)= (-4+ 2i)/2= -2+ i.

    Simplify (1+3i)/(1-i) by 'rationalizing' the denominator: (1+3i)(1+i)/(1-i)(1+i)= (-2+ 4i)/2= -1+ 2i.

    The sum is -3+ 3i.

    Your attempt to do things the "easy way" is what messed you up.
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