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Math Help - complex numbers

  1. #1
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    complex numbers

    given that z=5-7i and w=2<-pi/3

    1)State Im(z)
    2)arg(w)
    3)Modulo of w

    4)convert z to polar form and w to cartesain form

    5) calculate z-w
    zw
    z/w
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  2. #2
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    Re: complex numbers

    What do you mean by 2 <- pi/3?
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  3. #3
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    Re: complex numbers

    its in polar form, 2<pi/3 is an complex number with an angle of pi/3 and length of 2
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    Re: complex numbers

    Quote Originally Posted by Magical View Post
    its in polar form, 2<pi/3 is an complex number with an angle of pi/3 and length of 2
    Well then you need to write it as \displaystyle \begin{align*} 2\left(\cos{\frac{\pi}{3}} + i\sin{\frac{\pi}{3}}\right), 2\,\textrm{cis}\,\frac{\pi}{3} \end{align*} or \displaystyle \begin{align*} 2e^{i\frac{\pi}{3}} \end{align*}.

    Anyway, what have you gotten so far?
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  5. #5
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    Re: complex numbers

    exactly what uve got 2(cospi/3 +isinpi/3)
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  6. #6
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    Re: complex numbers

    I mean, what have you tried for the answers to your questions?
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  7. #7
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    Re: complex numbers

    i get 7 for part 1, dont know how to do part 2 or 3
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  8. #8
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    Re: complex numbers

    7 is incorrect. It's actually -7.

    As for part 2 and 3, the "modulus" of a complex number is its size or length. How long is \displaystyle \begin{align*} 2\left(\cos{\frac{\pi}{3}} + i\sin{\frac{\pi}{3}}\right) \end{align*}? The "argument" is the angle made. What is the angle in this complex number?
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  9. #9
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    Re: complex numbers

    the angle in the complex number is pi/3 and to find the length i would need to use root(a sqaured +b sqaures)
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  10. #10
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    Re: complex numbers

    Quote Originally Posted by Magical View Post
    the angle in the complex number is pi/3 and to find the length i would need to use root(a sqaured +b sqaures)
    You can. It's a bit pointless though. Any complex number in Polar form \displaystyle \begin{align*} r\left(\cos{\theta} + i\sin{\theta}\right) \end{align*} has a modulus of \displaystyle \begin{align*} r \end{align*}.
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