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Math Help - Converting to Trigonometric form

  1. #1
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    Converting to Trigonometric form

    I couldn't succeed converting the following complex number to it's trigonometric form, could someone help?
    √(2+√3) + i*√(2-√3)
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  2. #2
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    Quote Originally Posted by Fujiwara View Post
    I couldn't succeed converting the following complex number to it's trigonometric form, could someone help?
    √(2+√3) + i*√(2-√3)

    Put z=\sqrt{2+\sqrt{3}}+i\sqrt{2-\sqrt{3}}\Longrightarrow |z|^2=2+\sqrt{3}+2-\sqrt{3}=4,

    \arg(z)=\arctan\frac{\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}=\arctan\sqrt{7-4\sqrt{3}}=\frac{1}{12\pi} , so

    z=2cis(\frac{1}{12\pi})=2e^{i\frac{1}{12\pi}

    Tonio
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