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# Fp2 chapter 3 Loci of complex numbers question watch

1. Hi, I'm having some problems with the questions in fp2, an example of one would be:
sketch the locus of z when:arg (z-3i) - arg(z-5) = pi/4
in the example in the book, it says to do:

let arg (z-3i) = theta (i cant find the symbol)
arg (z-5) = alpha

theta - alpha = pi/4

then draw both individually on an argand diagram, and the loci is the circle round the points where they intersect.

In mostly okay with that I think, but what I don't understand is sometimes the line they draw for arg (z- whatever) has a positive gradient, and sometimes it has a negative gradient - i.e. sometimes they take theta to be obtuse and sometimes they take it to be accute, and the same for alpha.
How do you know whether theta/alpha is accute or obtuse, or when to use negative theta/alpha on your diagram?

Sorry I know I havent explained it very well but can anyone help?
2. (Original post by Emma09)
Hi, I'm having some problems with the questions in fp2, an example of one would be:
sketch the locus of z when:arg (z-3i) - arg(z-5) = pi/4
in the example in the book, it says to do:

let arg (z-3i) = theta (i cant find the symbol)
arg (z-5) = alpha

theta - alpha = pi/4

then draw both individually on an argand diagram, and the loci is the circle round the points where they intersect.

In mostly okay with that I think, but what I don't understand is sometimes the line they draw for arg (z- whatever) has a positive gradient, and sometimes it has a negative gradient - i.e. sometimes they take theta to be obtuse and sometimes they take it to be accute, and the same for alpha.
How do you know whether theta/alpha is accute or obtuse, or when to use negative theta/alpha on your diagram?

Sorry I know I havent explained it very well but can anyone help?
What the book is basically saying is:

let and

now if you try to draw it such that you will see it wont be possible, as (so the angle made by the two half lines will never be pi/4) hence let and (then which works as ) then you will see that it works, just draw it so that the angle made by the half lines is pi/4 and you will see how it works

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Updated: March 17, 2013
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