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

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|)

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

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

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.)

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

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?