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Math Help - Complex numbers - Subtraction of modulus in Argand diagram

  1. #1
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    Complex numbers - Subtraction of modulus in Argand diagram

    Hi, I am not sure if I should be posting here or on number theory, but there goes:

    I am supposed to show geometrically (using an Argand diagram) that, for two complex numbers z and w, |z + w| is equal or larger than |z| - |w|.
    It should follow the application of the triangle inequality (which is easy to show and I have no problem with).

    My problem is how do I represent the subtration of modulus of z minus modulus of w? Treating them as vectors I can find the modulus of their addition or subtraction, but not the subtraction of the moduli???

    Any suggestions would be greatly appreciated.

    Thanks,
    Maria
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  2. #2
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    Re: Complex numbers - Subtraction of modulus in Argand diagram

    Although z & w are complex numbers, but |z+w| as well as |z|-|w| are both real numbers. So on real axis of Argand circle display these values and prove your point from there.
    Thanks from mariab
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    Re: Complex numbers - Subtraction of modulus in Argand diagram

    Yes, that works. Specially if I represent the moduli as circles centered in O and then look at them when they intersect the real axis.

    Thanks a lot,
    Maria
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