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Math Help - Prove |w + z| <= |w| +|z|

  1. #1
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    Post Prove |w + z| <= |w| +|z|

    hi. Anyway we are studying imaginary/complex numbers and how to graph them and all and i have to answer a question that says:

    Look at the picture below and prove that:
    lZ+Wl (Less than or equal sign) lZl + lWl
    Thx

    Last edited by mr fantastic; March 1st 2010 at 02:04 AM. Reason: Changed post title
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  2. #2
    Member mathemagister's Avatar
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    Quote Originally Posted by mamann View Post
    hi. Anyway we are studying imaginary/complex numbers and how to graph them and all and i have to answer a question that says:

    Look at the picture below and prove that:
    lZ+Wl (Less than or equal sign) lZl + lWl
    Thx

    The line |Z+W|, as you call it, is, since it is a line, the shortest distance between its endpoints. Any other path from one endpoint to the other will be longer because the shortest distance between 2 points is a line.
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  3. #3
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    yea but our teacher said to prove it using the distance....um...
    well he said to use formulae and all that. including:
    Z=a+ib
    lZl= (root of)[ (a^2) + (b^2) ] and other calculations


    P.S: how do you put in equations
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by mamann View Post
    hi. Anyway we are studying imaginary/complex numbers and how to graph them and all and i have to answer a question that says:

    Look at the picture below and prove that:
    lZ+Wl (Less than or equal sign) lZl + lWl
    Thx

    It follows from the cosine rule for triangles since you have a triangle with sides |Z+W|, |Z| and |W|.

    CB
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