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Math Help - Euler's Formula

  1. #1
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    Euler's Formula

    Use Euler's Formula to write 2sq.rt.2 -2isq.rt.2 in exponential form.

    My answer: 4e^i(7pi/4)

    I just need confirmation that my answer is correct. Thanks.
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  2. #2
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    Quote Originally Posted by Joanie View Post
    Use Euler's Formula to write 2sq.rt.2 -2isq.rt.2 in exponential form.

    My answer: 4e^i(7pi/4)

    I just need confirmation that my answer is correct. Thanks.
    2\sqrt{2}-2i \sqrt{2} \not= 4e^{i*(7pi/4)}
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  3. #3
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    Euler's Formula

    I redid the problem: Use Euler's formula to write 2sqrt(2)-2isqrt(2) in exponential form.

    I was told by this forum that my answer 4e^i(7pi/4) is incorrect.

    Is 4e^i(pi/4) the correct answer? If not, where am I making the error?

    Thanks.
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  4. #4
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    Quote Originally Posted by Joanie View Post
    I redid the problem: Use Euler's formula to write 2sqrt(2)-2isqrt(2) in exponential form.

    I was told by this forum that my answer 4e^i(7pi/4) is incorrect.

    Is 4e^i(pi/4) the correct answer? If not, where am I making the error?

    No, this is wrong, too.

    It is

    a+ib = r*e^{i*\phi},

    where r^2 = a^2+b^2

    in this case: r^2 = (2\sqrt{2})^2+ (2\sqrt{2})^2= 4*2+4*2 = 16

    => r = 4

    and \phi = -arccos(a/r) (because a > 0, b <0)

    in this case \phi = -arccos(1) = -pi/4

    => 2\sqrt{2}-2i \sqrt{2} = 4e^{i*(-pi/4)} = 4cos(- pi/4) + 4sin(-pi/4)i

    Yours,
    Rapha
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