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Math Help - Complex no: Where did I go wrong

  1. #1
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    Complex no: Where did I go wrong

    Another one! I'm really sorry. This time I'm not sure where I went wrong.

    Express in polar form, (1/(sqrt(21) - sqrt(7)i)*)
    Conjugate, so I got (1/(sqrt(21) + sqrt(7)i))
    Let z = sqrt(21) + sqrt(7)i
    In modulus argument form ie. cis form, I got sqrt(30)cis(pi/6)
    For the modulus of (1/(sqrt(21) - sqrt(7)i)*),
    I got 1/sqrt(30)
    But the answer is (sqrt(7)/14)!

    Thank you very much for your time,
    J.
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  2. #2
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    Re: Complex no: Where did I go wrong

    Quote Originally Posted by Tutu View Post
    Another one! I'm really sorry. This time I'm not sure where I went wrong.

    Express in polar form, (1/(sqrt(21) - sqrt(7)i)*)
    Conjugate, so I got (1/(sqrt(21) + sqrt(7)i))
    Let z = sqrt(21) + sqrt(7)i
    In modulus argument form ie. cis form, I got sqrt(30)cis(pi/6)
    For the modulus of (1/(sqrt(21) - sqrt(7)i)*),
    I got 1/sqrt(30)
    But the answer is (sqrt(7)/14)!

    Thank you very much for your time,
    J.
    In order to convert to the polar form, the complex number first needs to be in Cartesian form.

    \displaystyle \begin{align*} \frac{1}{\sqrt{21} - i\sqrt{7}} &= \frac{\sqrt{21} + i\sqrt{7}}{\left( \sqrt{21} - i\sqrt{7} \right) \left( \sqrt{21} + i\sqrt{7} \right)} \\ &= \frac{\sqrt{21} + i\sqrt{7}}{\left( \sqrt{27} \right)^2 + \left( \sqrt{7} \right)^2 } \\ &= \frac{\sqrt{21} + i\sqrt{7}}{34} \\ &= \frac{\sqrt{27}}{34} + i\frac{\sqrt{7}}{34} \end{align*}

    Now that it's in \displaystyle \begin{align*} a + i\,b \end{align*} form, try converting to polars.
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  3. #3
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    Re: Complex no: Where did I go wrong

    Thank you very much!
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