[041087]

Hey, just started self-teaching fp1 yesterday and still on chapter one -complex numbers and this is the first exercise im having trouble with, and i haven't a clue how to do the following question

Find the real numbers x and y , given that : 1/(x+iy) = 3-2i?

This is my following steps:


i have no ideal what is the next step
if you could help me by showing the working that would be much appreciated

[notnek]

Rationalising the algebraic part is not needed here and makes things more complicated than they need to be.


The Comparing real and imaginary parts method would work better by doing this:



You should find that comparing real and imaginary parts from here is much easier.


Alternatively, you could change the equation to



and then rationalise the left hand side. This is probably the quickest method.

[Micky76]

(Original post by 041087)
Hey, just started self-teaching fp1 yesterday and still on chapter one -complex numbers and this is the first exercise im having trouble with, and i haven't a clue how to do the following question

Find the real numbers x and y , given that : 1/(x+iy) = 3-2i?

This is my following steps:


i have no ideal what is the next step
if you could help me by showing the working that would be much appreciated

Can I just ask what textbook do you study from?

[041087]

(Original post by Micky76)
Can I just ask what textbook do you study from?

[041087]

(Original post by notnek)
Rationalising the algebraic part is not needed here and makes things more complicated than they need to be.


The Comparing real and imaginary parts method would work better by doing this:



You should find that comparing real and imaginary parts from here is much easier.


Alternatively, you could change the equation to



and then rationalise the left hand side. This is probably the quickest method.

thanks

[aznkid66]

The long+weird way:

(I was bored. Also, don't hate on me detouring around all arithmetic that might include fractions. :P I hate fractions with a passion.)





Note: From here, you can go straight to . However, note that









Note: Quadratics are nice. ^-^

Spoiler:

Show

Note: y=x=0 is extraneous because of the denominator(s).