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Write in the form z=x+jy the complex number e^e^j ^=exp

  1. Oct 12, 2004 #1
    Can you help me with the following problems plz.
    I have a course in telecommunications and i have to understand
    complex numbers first.

    I can't solve the following exercises:
    1) Write in the form z=x+jy the complex number e^e^j

    2)how i can solve this equation |z+2|=|z-1| and what is the algebraical explanation (z=|z|e^jè|)
  2. jcsd
  3. Oct 12, 2004 #2


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    So what have you managed to do so far?
  4. Oct 12, 2004 #3
    nothing these are the only exercises of the assignment that i cant do
  5. Oct 13, 2004 #4
    1. Use Euler formula
    2. a. |z-2|=|z+1| <-- is it modular or absulute?
    b. so what do you think an algebraical form is ? (also use 1.)
  6. Oct 14, 2004 #5

    [tex]e^{j\phi} = \cos\phi + j\sin\phi[/tex]
    [tex]\Rightarrow e^{j} = \cos(1) + j\sin(1)[/tex]
    [tex]\Rightarrow e^{e^{j}} = e^{\cos(1) + j\sin(1)} = e^{\cos(1)}e^{j\sin(1)}[/tex]

    Can you take this further now?

  7. Oct 14, 2004 #6
    According to the second equation, viz [tex]\|z + 2\| = \|z - 1\|[/tex] a point is constrained to move on the Gaussian plane such that its distance from a fixed point -2 + j0 equals its distance from another fixed point 1 + j0. Do you know anything else about it or is that it? If you set z = x + jy and solve the resulting algebraic equation (which is quadratic in x), you get something like x = constant, but nothing about y.....did you try this?
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