The modulus

For the modulus like |x+y|:

How do you know when to just either
1. Take the positive value of x+y
OR
2. The square root of x squared + y squared

Many thanks

Reply 1

cksiu

Universities Forum Helper

Original post

by JibberJam

For the modulus like |x+y|:
How do you know when to just either
1. Take the positive value of x+y
OR
2. The square root of x squared + y squared
Many thanks

Always check your propositions, say x=+1, y=-1.

Reply 2

mqb2766

Original post

by JibberJam

For the modulus like |x+y|:
How do you know when to just either
1. Take the positive value of x+y
OR
2. The square root of x squared + y squared
Many thanks

Always

"Never"

Reply 3

Nitrotoluene

Original post

by JibberJam

For the modulus like |x+y|:
How do you know when to just either
1. Take the positive value of x+y
OR
2. The square root of x squared + y squared
Many thanks

You're going to try and do it alone, and I think that's the right way to do it. I'm sure it'll go well. Let's chew over our consideration of "modulus" and figure out in what situations the different approaches come into play.
When we talk about explaining the modulus of a number, for a real number, take (a). The symbol (|a|) means the distance kind of from zero on a number line, right? Now how do we actually get that value?
Now, we go to slightly more interesting part, namely complex numbers. It is well known pattern that a complex number (z) can be written as (z = x + iy) where (x) and (y) are just regular real numbers, and that little (i) is the imaginary unit (that tricky (sqrt{-1})).
Let's think about those two expressions you have there:
When does (|x + y|) just reduce to the positive version of (x + y)? What would have to be true about the numbers (x) and (y) for that to be the case?
And when do we use that (sqrt{x^2 + y^2}) to calculate (|x + y|)? How does the real part fit in with the imaginary? What does that tell you when you visualize it on that complex plane?
Hold on to these questions in the back of your mind, because they will be the secret to unlocking this. And if you get stuck or just want another little push, write me!
Here is my 2 cents!

Quick Reply

Latest

Trending

Articles for you

$What is LaTeX?$

What is LaTeX?

Personal Statement:Physics 36

How The Student Room is moderated

To keep The Student Room safe for everyone, we moderate posts that are added to the site.

Try out the app

Continue on web

The modulus

Quick Reply

Related discussions

Articles for you

How The Student Room is moderated