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Math Help - Complex Variable proof help

  1. #1
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    Complex Variable proof help

    Please help in provig the statement below

    arg ( z_1 / z_2) = arg ( z_1) - arg ( z_2)
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  2. #2
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    Re: Complex Variable proof help

    just write $z_1$ and $z_2$ in complex exponential form and the proof writes itself
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  3. #3
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    Re: Complex Variable proof help

    u can write z1=r1*e^(theta1) z2=r2*e^(theta2) therefore dividing both these u get (r1/r2)*e^(theta1-theta2) so argument=(theta1-theta2)
    now on rhs arg(z1)=theta1 and arg(z2)=theta2 so (theta1-theta2)
    l.h.s=r.h.s
    hence proved
    Thanks from flaming
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  4. #4
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    Re: Complex Variable proof help

    Quote Originally Posted by flaming View Post
    Please help in provig the statement below

    arg ( z_1 / z_2) = arg ( z_1) - arg ( z_2)
    Do you know that $\dfrac{1}{z} = \dfrac{{\overline z }}{{{{\left| z \right|}^2}}}$ and $\text{arg}(\overline{z})=-\text{arg}(z)~?$

    Most textbooks authors use some variation of that.
    Thanks from topsquark and flaming
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