Complex Numbers Equation with Real Solutions

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Homework Help Overview

The problem involves finding real numbers p and q that satisfy a complex equation involving Euler's formula. The equation is presented in a form that includes both real and imaginary components, prompting a discussion on how to isolate and equate these components.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to convert the right side of the equation to rectangular form and solve for p, but expresses uncertainty about the next steps. Some participants suggest equating the real part of the equation to p and setting the imaginary part to zero, leading to specific values for p and q.

Discussion Status

The discussion includes various interpretations of how to approach the problem, with some participants proposing potential values for p and q based on their reasoning. There is a lack of explicit consensus, but some guidance has been offered regarding the relationship between the real and imaginary parts of the equation.

Contextual Notes

Participants are working under the assumption that p and q must be real numbers, and there may be constraints related to the simplification of complex expressions.

atarr3
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Homework Statement



Find real numbers p and q such that the following equation is true:

[tex]\frac{p}{q+5i}=4e^{\frac{-i\pi}{4}}[/tex]

Homework Equations



Euler's formula

The Attempt at a Solution



Ok so I converted the right side to rectangular form using Euler's formula and solved for p. But I don't really know what do after that.

I got [tex]p=5\sqrt{2}q+25\sqrt{2}+25i\sqrt{2}-5qi\sqrt{2}[/tex] but I don't know how to simplify this any further.
 
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Maybe [tex]p[/tex] is equal to the real part of the right side and the imaginary part must equal zero. Which would make [tex]q=5[/tex] and [tex]p=50\sqrt{2}[/tex]?
 
atarr3 said:
Maybe [tex]p[/tex] is equal to the real part of the right side and the imaginary part must equal zero. Which would make [tex]q=5[/tex] and [tex]p=50\sqrt{2}[/tex]?
Yep, that'll do it.
 
Haha ok thank you. I guess I didn't need to post this after all.
 

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