# Difficult complex numbers

• Dec 2nd 2008, 11:04 AM
djmccabie
Difficult complex numbers
The complex numbers Z and W are represented, respectively, by points P(x, y) and Q(u,v) in Argand diagrams and

W=1/(Z+1)

By first writing Z+1=1/W

(a) Show that

x+1=u/(u²+v²)

and find an expression for y in terms of u and v.

(b) The point P moves along the circle (x+1)² + y² = 4. Find the equation of the locus Q.

Could somebody please show a step by step solution to this please? I really don't know how to answer these type of questions. Is there a general method?

Thanks

Dan
• Dec 2nd 2008, 11:13 AM
Plato
$\displaystyle \left( {x + 1} \right) + yi = Z + 1 = \frac{1} {w} = \frac{{\overline w }} {{\left| w \right|^2 }} = \frac{{u - vi}} {{u^2 + v^2 }}$
From there you should be able to finish.
• Dec 2nd 2008, 02:28 PM
djmccabie
Hi that does not help at all. does anybody have a step by step solution?

thanks

dan
• Dec 2nd 2008, 03:28 PM
Plato
Quote:

Originally Posted by djmccabie
Hi that does not help at all. does anybody have a step by step solution?

I am awfully sorry that you did not find that rather straightforward answer did not help you.
Also, I hope that you are not expecting to be given a step-by-step, ready to hand in, solution.
If that is what you want then you are short selling yourself.
You should want to learn the concepts involved here.

You need to see that the real part of the left side must equal the real part of the right. Likewise the imaginary part of the left side must equal the imaginary part of the right side.
• Dec 2nd 2008, 03:39 PM
djmccabie
I'm not after a solution to hand it. I just dont like my teachers method and seek an alternative.You may find this straightforward but i dont. I'm sure sending condescending posts like this should be against rules.
• Dec 2nd 2008, 04:12 PM
Jameson
Quote:

Originally Posted by djmccabie
I'm not after a solution to hand it. I just dont like my teachers method and seek an alternative.You may find this straightforward but i dont. I'm sure sending condescending posts like this should be against rules.

Why would you purposefully try to break the rules and not be able to get help?

Look - if you want or need another view after a member has provided help then make another post SHOWING SOME KIND OF WORK. The more you seem actually interested in learning instead of having someone give you answers, the more you'll get help I'm sure.

Good luck.