Solving Complex Equations Involving a,b,c,p,q,r

  • Thread starter juantheron
  • Start date
  • Tags
    Complex
In summary, the given equations involve complex numbers \mathbf{a,b,c,p,q,r} and ask for the value of \displaystyle\mathbf{\frac{p^2}{a^2}+\frac{q^2}{b^2}+\frac{r^2}{c^2}}. By correcting a mistake in one of the equations and simplifying, the value can be determined to be 2i.
  • #1
juantheron
247
1

Homework Statement



If [tex]\mathbf{a,b,c,p,q,r}[/tex] are complex number

Homework Equations


and [tex]\displaystyle\mathbf{\frac{p}{a}+\frac{q}{b}+\frac{r}{c} = 1+i}[/tex]

and [tex]\displaystyle\mathbf{\frac{a}{b}+\frac{b}{q}+\frac{c}{r} = 0}[/tex].Then find value of

[tex]\displaystyle\mathbf{\frac{p^2}{a^2}+\frac{q^2}{b^2}+\frac{r^2}{c^2}=}[/tex]


The Attempt at a Solution



No idea
 
Physics news on Phys.org
  • #2
juantheron said:

Homework Statement



If [tex]\mathbf{a,b,c,p,q,r}[/tex] are complex number

Homework Equations


and [tex]\displaystyle\mathbf{\frac{p}{a}+\frac{q}{b}+\frac{r}{c} = 1+i}[/tex]

and [tex]\displaystyle\mathbf{\frac{a}{b}+\frac{b}{q}+\frac{c}{r} = 0}[/tex].
I think you have a mistake in the equation above. I believe it should be
[tex]\frac{a}{p}+\frac{b}{q}+\frac{c}{r} = 0[/tex]

I made that change and was able to get a value of 2i for the expression you want to evaluate. What I did was to square both sides of the equation whose right side is 1 + i. If you work with the other equation, as corrected above, you can substitute it in the other equation to arrive at a simplified result.
juantheron said:
Then find value of

[tex]\displaystyle\mathbf{\frac{p^2}{a^2}+\frac{q^2}{b^2}+\frac{r^2}{c^2}=}[/tex]


The Attempt at a Solution



No idea
 
  • #3
Thanks Mark44.
 

1. How do I solve complex equations involving a,b,c,p,q,r?

To solve complex equations involving a,b,c,p,q,r, you need to follow a systematic approach. First, simplify the equation by combining like terms. Then, use the distributive property to remove any parentheses. Next, isolate the variable you are solving for on one side of the equation, and move all other terms to the other side. Finally, solve for the variable using appropriate algebraic operations.

2. What do a, b, c, p, q, and r represent in complex equations?

In complex equations, a, b, c, p, q, and r represent variables. These variables are used to represent unknown quantities in the equation. They can take on any value, and their values can change depending on the given equation.

3. How do I determine if a complex equation has a solution?

To determine if a complex equation has a solution, you need to solve the equation and see if it satisfies the given conditions. If the final value for the variable satisfies all the given conditions, then the equation has a solution. If the final value does not satisfy the conditions, the equation has no solution.

4. What are some common mistakes to avoid when solving complex equations?

Some common mistakes to avoid when solving complex equations include not properly simplifying the equation, forgetting to perform operations on both sides of the equation, and making calculation errors. It is also important to check the final solution to ensure it satisfies all the given conditions.

5. Can I use a calculator to solve complex equations?

Yes, you can use a calculator to solve complex equations. However, it is important to understand the steps involved in solving the equation manually to ensure you input the correct equation and use the correct operations on the calculator. Additionally, calculators may not be able to solve certain types of complex equations, so it is always good to have a solid understanding of the manual process.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
3
Views
468
  • Precalculus Mathematics Homework Help
Replies
7
Views
810
  • Precalculus Mathematics Homework Help
Replies
20
Views
1K
  • Precalculus Mathematics Homework Help
Replies
4
Views
3K
  • Precalculus Mathematics Homework Help
Replies
8
Views
960
  • Precalculus Mathematics Homework Help
Replies
1
Views
853
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Electromagnetism
Replies
11
Views
959
  • Precalculus Mathematics Homework Help
Replies
8
Views
539
Replies
27
Views
2K
Back
Top