# Prove |w + z| <= |w| +|z|

• Feb 28th 2010, 05:15 AM
mamann
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

http://img7.imageshack.us/img7/9076/mathproblemy.jpg
• Feb 28th 2010, 05:31 AM
mathemagister
Quote:

Originally Posted by mamann
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

http://img7.imageshack.us/img7/9076/mathproblemy.jpg

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.
• Feb 28th 2010, 05:43 AM
mamann
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
• Feb 28th 2010, 05:44 AM
CaptainBlack
Quote:

Originally Posted by mamann
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

http://img7.imageshack.us/img7/9076/mathproblemy.jpg

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

CB