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

[juantheron]

Homework Statement

If $$\mathbf{a,b,c,p,q,r}$$ are complex number

Homework Equations

and $$\displaystyle\mathbf{\frac{p}{a}+\frac{q}{b}+\frac{r}{c} = 1+i}$$

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

$$\displaystyle\mathbf{\frac{p^2}{a^2}+\frac{q^2}{b^2}+\frac{r^2}{c^2}=}$$

The Attempt at a Solution

No idea

 

[Mark44]

Homework Statement

If $$\mathbf{a,b,c,p,q,r}$$ are complex number

Homework Equations

and $$\displaystyle\mathbf{\frac{p}{a}+\frac{q}{b}+\frac{r}{c} = 1+i}$$

and $$\displaystyle\mathbf{\frac{a}{b}+\frac{b}{q}+\frac{c}{r} = 0}$$.

I think you have a mistake in the equation above. I believe it should be
$$\frac{a}{p}+\frac{b}{q}+\frac{c}{r} = 0$$

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.

Then find value of

$$\displaystyle\mathbf{\frac{p^2}{a^2}+\frac{q^2}{b^2}+\frac{r^2}{c^2}=}$$

The Attempt at a Solution

No idea

 

[juantheron]

Thanks Mark44.