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    I was looking through a solution to a question and found this:


    what are the rules for modulus functions? wouldn't the norm be to separate the fraction using |w+1-3i|-|2| rather than multiplying by 2?

    slightly confused, sorry if its a trivial question :/
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    Both sides of the equation have been multiplied by 2? I'm not sure what you mean by "separate the fraction using |w+1-3i| - |2|"?

    EDIT: And what do you mean about the "rules for modulus functions"?. In general,  |ab| = |a||b| ,  \left|\frac{a}{b}\right| = \frac{|a|}{|b|} but  |a+b| \neq |a| + |b|
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    Basically the modulus function turns something negative into a positive:- if you did the modulus of '-1' you would get '1'. Since 2 is already a positive number the modulus brackets can be ignored and you just re-arrange the equation as normal.

    This only changes when you have got a variable though, as there are different possible solutions then, depending upon the size of the variable.
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    (Original post by ashleyb123)
    I was looking through a solution to a question and found this:


    what are the rules for modulus functions? wouldn't the norm be to separate the fraction using |w+1-3i|-|2| rather than multiplying by 2?

    slightly confused, sorry if its a trivial question :/
    I think you're confusing this with the idea of the argument of the quotient of two complex numbers. i.e. \arg \left(\dfrac{z_1}{z_2}\right) = \arg (z_1) - \arg (z_2) + 2k\pi, where k\in\{-1,0,1\} and is chosen to ensure that the resulting argument follows whichever convention you are following i.e. the \pi-convention, 2\pi-convention etc.

    A modulus is just a real number so it's fine to just multiply both sides by it.
 
 
 
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