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# Locus of argument of complex numbers watch

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1. So I get that the argument locus can be used to form a line so arg(z) = theta forms a line with an angle of theta between itself and the positive real axis.

What I don't get is the statement that 'the locus of points satisfying arg(z-z1)=theta is a half-line from the point z1 at an angle of theta to the positive real axis'.

What is a half-line? Is it simply a line that terminates at the given point (z1)?
2. (Original post by AmmarTa)
So I get that the argument locus can be used to form a line so arg(z) = theta forms a line with an angle of theta between itself and the positive real axis.

What I don't get is the statement that 'the locus of points satisfying arg(z-z1)=theta is a half-line from the point z1 at an angle of theta to the positive real axis'.

What is a half-line? Is it simply a line that terminates at the given point (z1)?
Yes that's basically what a half line is - it extends from a point in one direction only. I highly recommend this video, which explains everything fully.
3. (Original post by Notnek)
Yes that's basically what a half line is - it extends from a point in one direction only. I highly recommend this video, which explains everything fully.
Thanks, your explanation cleared it up plus the video helped me to further understand!

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