# Complex numbers - Subtraction of modulus in Argand diagram

• Aug 28th 2012, 09:02 AM
mariab
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
• Aug 28th 2012, 09:29 AM
MaxJasper
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.
• Aug 28th 2012, 10:32 AM
mariab
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