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Math Help - finding r, absolute value of (sqrt3 + i)

  1. #1
    Junior Member BugzLooney's Avatar
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    finding r, absolute value of (sqrt3 + i)

    I was doing some reading through the forum and noticed a question about De Moivre's theorem and realized that I don't know how to find r at all.

    I was wondering why the radius is 2 when you take the absolute value of (sqrt3 + i)
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  2. #2
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    For \displaystyle x+yi \implies r =\sqrt{x^2+y^2}

    so \displaystyle \sqrt{3}+i \implies r =\sqrt{(\sqrt{3})^2+1^2} =\sqrt{4}=2
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  3. #3
    Junior Member BugzLooney's Avatar
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    Is this the form that all of these types of questions are in? I mean would it be possible to see a question asking for the absolute value of (sqrt3 + i) without any hints of r or anything?
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    Any question where you need to find the solutions of a complex equation using De Moivre's would assume r is needed.
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  5. #5
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    Quote Originally Posted by BugzLooney View Post
    Is this the form that all of these types of questions are in? I mean would it be possible to see a question asking for the absolute value of (sqrt3 + i) without any hints of r or anything?
    You could be required to calculate the "modulus" of a complex number.

    On an Argand Diagram, a complex number's "modulus" is it's distance from the origin (0,0).

    Pythagoras' theorem calculates this
    [you can draw a right-angled triangle with hypotenuse being the line from (0,0) to z].

    z=a+ib

    r^2=|z|^2=a^2+b^2\Rightarrow\ |z|=r=\sqrt{a^2+b^2}
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  6. #6
    Member rtblue's Avatar
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    For any further questions you might have, I find this video to be very informative:

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