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

  • Thread starter dionys
  • Start date
  • #1
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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
^=exp

2)how i can solve this equation |z+2|=|z-1| and what is the algebraical explanation (z=|z|e^jè|)
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
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So what have you managed to do so far?
 
  • #3
10
0
nothing these are the only exercises of the assignment that i cant do
 
  • #4
43
0
dionys said:
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
^=exp

2)how i can solve this equation |z+2|=|z-1| and what is the algebraical explanation (z=|z|e^jè|)
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.)
 
  • #5
1,789
4
Hello

[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?

Cheers
Vivek
 
  • #6
1,789
4
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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