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

1. Oct 12, 2004

### dionys

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|)

2. Oct 12, 2004

### Hurkyl

Staff Emeritus
So what have you managed to do so far?

3. Oct 12, 2004

### dionys

nothing these are the only exercises of the assignment that i cant do

4. Oct 13, 2004

### Motifs

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. Oct 14, 2004

### maverick280857

Hello

$$e^{j\phi} = \cos\phi + j\sin\phi$$
$$\Rightarrow e^{j} = \cos(1) + j\sin(1)$$
$$\Rightarrow e^{e^{j}} = e^{\cos(1) + j\sin(1)} = e^{\cos(1)}e^{j\sin(1)}$$

Can you take this further now?

Cheers
Vivek

6. Oct 14, 2004

### maverick280857

According to the second equation, viz $$\|z + 2\| = \|z - 1\|$$ 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?