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Math Help - Complex Numbers

  1. #1
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    Complex Numbers

    Write each of the given numbers in the form a+bi

    a) (e^(9i)-e^(-9i))/(2i)

    b) 2e^(9+((i*pi)/6))

    I don't even know how to start...

    thanks in advance!!
    (
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  2. #2
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    On the a) part, use the fact that cosine is an even function and sine is an odd function.
    Then \begin{gathered} e^{9i} = \cos (9) + i\sin (9) \hfill \\<br />
e^{ - 9i} = \cos ( - 9) + i\sin ( - 9) = \cos (9) - i\sin (9) \hfill \\ <br />
\end{gathered} .
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  3. #3
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    Complex numbers - Euler's Formula

    Hi -

    You'll need to use Euler's Formula:

    e^ix = cos(x) + i sin(x)

    Then use the fact that cos(-x) = cos(x) and sin(-x) = -sin(x) to simplify the result.

    It's also useful to note that e^(p + qi) = e^p . e^qi.

    Is that any help?
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  4. #4
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    Thanks!! =)

    One more question,
    I just don't know what they're asking and why two of the data points have two numbers and why the last one has three...
    Find a (complex) quadratic polynomial P(z) = a+bz+cz^2 which interpolates the data (-1,i), (0,i), and (5,i,0)

    Write your answers in Cartesian form x=iy
    a=
    b=
    c=
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  5. #5
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    Complex numbers - quadratic

    Hi -

    I'm not sure what they're asking either. Perhaps we want a quadratic for y in terms of x: y = a + b.x + c.x^2, given (x, y) pairs as follows:

    (-1, i), (0, i), and (5 + i, 0)

    This does make sense. If this is what is wanted, just substitute for x and y for each of the three pairs of values, and solve the three equations for a, b and c.

    In any event, I really don't know what (5,i,0) means unless we have a point in three dimensions whose coordinates are (x, y, z). (But then why are the other two only given as (x, y) pairs?)
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