Finding $z$ for a Complex Equation

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Homework Help Overview

The discussion revolves around finding all complex numbers \( z \) that satisfy the equation \( z = \exp(2 + 3i) \). The subject area is complex analysis, specifically focusing on the representation of complex numbers in exponential form.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to determine the modulus and argument of the complex number and questions the next steps in the process. Other participants confirm the uniqueness of the solution and explore whether the result should be expressed in the standard form \( a + bi \).

Discussion Status

The discussion is active with participants confirming the original poster's understanding of the modulus and argument. There is a suggestion to express the solution in \( a + bi \) form, indicating a productive exploration of representation.

Contextual Notes

Participants are navigating the requirements of expressing the solution in a specific format, which may be influenced by homework guidelines or expectations.

fauboca
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How do I find all $z$ that satisfies:

z = \exp\left(2+3i\right)

I know the modulus has to be e^2 and the argument has to be 3 but where do I go from there?
 
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That's it. There's only one z equal to that z.
 
LCKurtz said:
That's it. There's only one z equal to that z.

That is really all there is to it?
 
fauboca said:
That is really all there is to it?

Maybe you are supposed to write it in a+bi form?
 
LCKurtz said:
Maybe you are supposed to write it in a+bi form?

Yes that is correct.
 

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