Multiply both sides by 1+pi
Then you get...
3 + 5i = (1 + pi)(q + 4i) = q + pqi + 4i - 4p
=> 3 + 5i = (q - 4p) + 4i + pqi
=> 3 + i = (q - 4p) + pqi
So you want to solve...
q - 4p = 3
pq = 1
Hello,
I am having trouble with this question:
"Find all possible real number pairs p, q such that 3+5i/1+pi =q+4i"
Im sure it's easy but I think I am overlooking something. I multiplied both sides by the conjugate of 1+pi....ie.(1-pi) but I think it's wrong.
Any help would be appreciated.
Regards,
Neverquit
I think you are misinterpreting your own answer. When you solve the system of equations, you will find that
These are two separate solutions, not a single solution. You need to find the value of that pairs with each of these solutions for . So, you need to plug each value of back into the system of equations and find the corresponding values of . Since , it's a pretty straightforward calculation:
Therefore, the solutions are:
First solution:
Second solution:
You might also write this as:
But you definitely would not say that the solutions are and .
Having Plato and CP post in this thread has made me question whether my answer is wrong. Is it?
Solving the equations I arrived at...
q - 4p = 3
pq = 1
gives
q=1/p,
So subbing that into the first equation will give you a polynomial (if you multiply both sides by p) which gives you p = 1/4 and -1.
Hence q = 4 and -1.
Solutions are (1/4,4) and (-1, -1)
Are these the only solutions? Why must you multiply the top and bottom by the conjugate?
I think the solution that Plato gives using the congugate is what the text books author had in mind as the question is shortly after conjugates of complex numbers is explained.
Deastar, your solution still gives the same answer in the text book so it must be correct.
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