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# FP2: Finding Loci of Complex Numbers watch

1. Hi! I've been struggling with this question for an hour. I have no way of figuring it out.
The question is: lzl = 1-sin (arg z)
Now I've made an assumption that sin (arg z) = (y/ square root(x^2 +y^2)), and that the graph should produce a spiral? Can some body help me out?

Thanks a bunch!
2. (Original post by PimL)
Hi! I've been struggling with this question for an hour. I have no way of figuring it out.
The question is: lzl = 1-sin (arg z)
Now I've made an assumption that sin (arg z) = (y/ square root(x^2 +y^2)), and that the graph should produce a spiral? Can some body help me out?

Thanks a bunch!
It won't be a spiral, as the pattern will repeat every 2(pi) radians. This looks as though it should be analogous to r = 1 - sin(@), which I think is a so called "cardioid" (heart shaped) curve aligned with the dimple at the top. A few trial values of @ and a polar sketch should confirm it one way or the other.

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Updated: October 13, 2017
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