I have a function $f(z)=\frac{6z}{(1+3i)z-4i}$ and I want to map the set $R^*$ using the function $f(z)$; how can I do it? I have written $f(z)$ into $x,y$ form as $$w=\frac{6(x+iy)}{(1+3i)(x+iy)-4i}$$ now if I put $y=0$ into this function I get $$w=\frac{6x}{(1+3i)(x)-4i}$$ How do I use this to find the image under $f$? I'm also uncertain how to sketch this.
2026-03-25 15:51:31.1774453891
Mapping extended set of real numbers under fractional linear transformations??
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