A few weeks back, I conducted a weekend of lessons on the modulus sign (or absolute value sign) with all my JC2. Its to prepare them for the upcoming prelims and A-levels. Many students till today, are still having difficulties with the modulus sign. I thought I will start a little series, just like the integration to introduce some misconceptions.
So what does modulus do? We know that 
, so it pretty much makes everything negative, positive. Is that it? This is a very loose representation of modulus (absolute) function. I usually tell my students to think of modulus like magnitude. We are really interested in the magnitude to 
here, and that will simply be 
. Why do I choose such a representation? Simply because it is the actual meaning!! Applying a modulus, is seeking the magnitude.
It so happen that is a scalar quantity. And when we talk about 
, we are applying pythagoras’ theorem here to find the magnitude. This is slightly different because 
is no longer a scalar, but a vector!
I hope clarifies your doubts about what exactly does modulus mean!
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