The line y= 3x corresponds to the set of complex number a+ 3ai= a(1+ 3i) for a any real number (do you see why?). . Now you could, if you wanted, multiply that out directly or use the "polar form". It will, in any case, be a constant, say u+ vi, so which gives "parametric" equations [/tex]y= va^5[/tex] and . (as long as u is not 0) so another straight line. Similarly for y= x/2 which corresponds to the set of complex numbers .
That is, maps that region, bounded by straight lines, into another region bounded by straight lines. You will need to compute and to determine exactly which straight lines.