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Differentiating complex numbers

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    Hi
    I'm having some difficulty with this simple question:
    'Determine for what values of z (if any) the function f(z) = |z| is differentiable.'

    My attempt:
     

z=x+iy

\lvert{z}\rvert=\sqrt{x^2+y^2} \in \mathbb{R}

which is differentiable at points where x^2+y^2 >0
    Is this right? It seems too simple. Have I misunderstood the question?
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    modulus of z is root X^2 - Y^2 as i^2 = -1

    Then I'm not sure, but I'm thinking you would differentiate implicitly by the chain rule if thats possible.
    Is this FP2?
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    (Original post by Taurus)
    modulus of z is root X^2 - Y^2 as i^2 = -1

    Then I'm not sure, but I'm thinking you would differentiate implicitly by the chain rule if thats possible.
    Is this FP2?
    That's not right, the modulus of x+iy is \sqrt{x^2+y^2}. It's the distance from the origin (in the Argand diagram) of x+iy, which corresponds to the point (x,y).

    By the looks of it this is first (maybe second) year undergraduate; differentiability definitely isn't in A-level!

    (Original post by Muffin.)
    Hi
    I'm having some difficulty with this simple question:
    'Determine for what values of z (if any) the function f(z) = |z| is differentiable.'

    My attempt:
     

z=x+iy

\lvert{z}\rvert=\sqrt{x^2+y^2} \in \mathbb{R}

which is differentiable at points where x^2+y^2 >0
    Is this right? It seems too simple. Have I misunderstood the question?
    You just seem to have stated the answer without proving it. Plug it into the definition of differentiability and take some limits to justify your claim.
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    nooooo please dont say maths gets this hard!
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    [QUOTE=nuodai;37162583]That's not right, the modulus of x+iy is \sqrt{x^2+y^2}. It's the distance from the origin (in the Argand diagram) of x+iy, which corresponds to the point (x,y).

    oh crap I knew that....
  6. Offline

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    Have you done the Cauchy-Riemann differential equations?

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