How to solve two equations involving complex variables?

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Discussion Overview

The discussion revolves around solving two simultaneous equations involving complex variables, specifically in the context of electrical circuits. Participants explore methods for solving these equations both manually and using a scientific calculator.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant requests methods for solving two equations involving complex variables, specifically asking for both manual and calculator methods.
  • Another participant seeks clarification on the notation used, questioning the meaning of "j4" and "j2" and suggesting they might represent powers of the imaginary unit.
  • A participant explains that "j" is used in circuit theory to denote the imaginary unit, clarifying that it does not represent powers of "i".
  • There is a discussion about the significance of complex coefficients in the equations, with one participant noting that they represent reactive components in a circuit.
  • Another participant proposes solving the equations by separating the real and imaginary parts, questioning whether the variables Ix and Iy are simply numbers or if they have specific meanings related to currents.
  • A participant provides a calculation for Ix, expressing concern about potential mistakes and inviting verification of their work.
  • One participant confirms the correctness of the calculation provided by another.

Areas of Agreement / Disagreement

Participants generally agree on the notation and the context of the equations, but there are differing views on the relevance of complex coefficients and the methods for solving the equations. The discussion remains unresolved regarding the best approach to solve the equations.

Contextual Notes

Some participants express uncertainty about the implications of using complex numbers in the equations and the specific meanings of the variables involved. There is also a lack of consensus on the most effective method for solving the equations.

shaiqbashir
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how to solve two equations involving complex variables??

Hi guys!

well! i want to know how can u solve the following two equations simultaenously in order to find out Ix and Iy:


(3+j4)Ix - j4Iy=10-------------(1)
(2-j4)Ix +j2Iy=0---------------(2)

please tell me the best methods to solve these two equations. How can i solve them with my scientific calculator?

Please tell me both ways:

solving manually

and solving through scientific calculator.

I shall be thankful to u for this act of kindness.

Take carez!

Good Bye!
 
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What do "j4" and "J2" mean? I assume j is your engineer's way of writing the imaginary unit that I would call i, but what are the 4 and 2 after them. If they are intended to mean powers, i^4 and i^2, then i2= -1 and i4= 1, of course.
 


HEy it's the way we write in circuits. I am looking for the same thing, how do you solve equations involving complex numbers by hand? My calculator doesn't do it.

So according to his equation, it means:

(3+4i) Ix - 4i Iy=10-------------(1)
(2-4i) Ix +2i Iy=0---------------(2)

And it's not a square of i. Please explain. Thanks.
 


We use j instead of i in circuits. And 3i is written as j3. It means the same.
 


@sonutulsiani,
And what about that big 'I'? What is meant by Ix, Iy etc?
 


Ix and Iy are currents. Do you know how to solve?
 


You posed your question as if the fact the coefficients are complex numbers with nonzero imaginary parts is relevant. Why?
 


Hurkyl said:
You posed your question as if the fact the coefficients are complex numbers with nonzero imaginary parts is relevant. Why?

I didn't understand what you said.
 


It's just algebra, you have two equations in two unknowns. You can solve for Ix in terms of Iy and then do substitution.

The complex coefficients you have represent the reactive components in your circuit, if they don't end up canceling then your currents will be out of phase with your voltage and how far out they are will be determined by the angle you get when you change your answers to polar form.
 
  • #10


Can't we solve it by separating the real and imaginary parts both on the left and right hand side of the equation?
 
  • #11


sonutulsiani said:
Ix and Iy are currents. Do you know how to solve?

I don't know about currents...all I'm asking whether they are numbers (here variables) or not. If they are just variables (I would like x instead of Ix and y instead of Iy), then it is very easy to solve. (No need to separation). I'm finding the value of Ix below and hope you will be able to follow:

(equation 1).(2i)-(equation 2). (-4i) gives

Ix=[20i]/[(3+4i).2i+(2-4i).4i]=[10]/[(3+4i)+4-8i]=10/(7-4i)=10(7+4i)/(49+16)=(14/13)+(8/13)i

Please check, I may have done any silly mistake in calculation.

Regards,
 
  • #12


your answer is correct.
 

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