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A diagram for the complex plane with equal scale on both axes (circles look like circles): the picture is sized from the ranges, unit grid, axes labelled Re and Im. Returns the diagram for the calls below. pixelsPerUnit defaults to 60 (less for a wide range).
xmin (number) -- xmax (number) -- ymin (number) -- ymax (number) -- pixelsPerUnit (number) -- optionalA dot at the complex number z with an optional label, placed clear of the dot on the side away from the origin.
d (diagram) -- z (complex) -- label (text) -- optionalcolor (text) -- a colour; the default is blueAn arrow from z1 to z2 (a complex number as the vector from 0 is argandVectorOn(d, 0, z)), with an optional label beside its middle.
d (diagram) -- z1 (complex) -- z2 (complex) -- color (text) -- a colour; the default is bluelabel (text) -- optionalA polygon through a list of complex numbers, lightly filled (fill defaults to the colour at 14%).
d (diagram) -- points (list of complex) -- color (text) -- a colour; the default is bluefill (text) -- optionalThe unit circle |z| = 1 in grey.
d (diagram) -- color (text) -- a colour; the default is blueThe n-th roots of unity: the unit circle, the regular n-gon through them, a dot at each and its label 1, ω, ω², ... (labels for n up to 16).
d (diagram) -- n (integer) -- 3 to 360color (text) -- a colour; the default is blueThe locus |z - a| kind r. "=" the circle; "<" the open disc (dashed boundary), "<=" the closed disc (solid), ">" and ">=" the outside. Regions are lightly filled and cut to the ranges.
d (diagram) -- a (complex) -- centrer (number) -- kind (text) -- "=" the curve, "<" or "<=" inside / near side, ">" or ">=" outside / far side; strict signs give a dashed boundarycolor (text) -- a colour; the default is blueThe locus arg(z - a) = theta: the ray from a at angle theta (radians) to the edge of the view, an open dot at a (a is left out).
d (diagram) -- a (complex) -- theta (number) -- radianscolor (text) -- a colour; the default is bluelabel (text) -- optionalThe region theta1 < arg(z - a) < theta2 (radians), filled, with both rays dashed and an open dot at a.
d (diagram) -- a (complex) -- theta1 (number) -- theta2 (number) -- color (text) -- a colour; the default is blueThe locus |z - a| + |z - b| kind k with foci a and b: the ellipse, its inside or outside. k must exceed |a - b| (the segment case is refused).
d (diagram) -- a (complex) -- b (complex) -- k (number) -- kind (text) -- "=" the curve, "<" or "<=" inside / near side, ">" or ">=" outside / far side; strict signs give a dashed boundarycolor (text) -- a colour; the default is blueThe locus |z - a| kind |z - b|: "=" the perpendicular bisector of a and b; "<" the side nearer a; ">" the side nearer b (filled, boundary dashed when strict).
d (diagram) -- a (complex) -- b (complex) -- kind (text) -- "=" the curve, "<" or "<=" inside / near side, ">" or ">=" outside / far side; strict signs give a dashed boundarycolor (text) -- a colour; the default is blueThe half-plane Re(z) kind c or Im(z) kind c, filled, with its boundary line dashed when the sign is strict.
d (diagram) -- part (text) -- "Re" or "Im"c (number) -- kind (text) -- "=" the curve, "<" or "<=" inside / near side, ">" or ">=" outside / far side; strict signs give a dashed boundarycolor (text) -- a colour; the default is blueDraws a region from its condition, as written: "|z - a| < r", "|z + 1 - i| >= 2", "|z - a| < |z - b|", "Re(z) >= 1", "Im(z) < 2" (= for the curve itself). Other conditions are refused.
d (diagram) -- condition (text) -- color (text) -- a colour; the default is blue