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Math Help - divide and express equation in standard form

  1. #1
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    divide and express equation in standard form

    divide and express the following equation in standard form, can someone explain to me how to do this.



    thanks in advance
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  2. #2
    Senior Member vincisonfire's Avatar
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    You must multiply by the conjugate.
     \frac{1}{a+bi}= \frac{1}{a+bi}\cdot \frac{a-bi}{a-bi} = \frac{a-bi}{a^2-b^2}
     \frac{a}{a^2-b^2}-\frac{bi}{a^2-b^2}
    You can also use the polar form (Euler notation)
    *re^{i\theta}
    In your case the top part is  2e^{0}=2 and the bottom part \sqrt{3^2+1}e^{i arctan\frac{-1}{3}} \simeq \sqrt{10}e^{-0.3218i} You are thus going to end with \frac{2}{ \sqrt{10}e^{-0.3218i}}=\frac{2e^{0.3218i}}{ \sqrt{10}}  \frac{2}{ \sqrt{10}}(cos(0.3218)+isin(0.3218))
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  3. #3
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    Thanks for the fast reply, can you verify if this is correct

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    Senior Member vincisonfire's Avatar
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    Replace i^2 by its value and simplify and ... you're done.
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  5. #5
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    ok thanks, but I wasn't given a value for i
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  6. #6
    Senior Member vincisonfire's Avatar
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    *i = \sqrt{-1} *This is among the most important number in mathematics. Remember its definition.
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  7. #7
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    ok thank you very much for your assistance
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