Complex numbers
Lab: modulus, distance and argument
Drag the points to connect coordinates, lengths and directions. Distinguish a circle from a disk and exact formulas from approximations.
Problem statement
Comparison in the complex plane
Drag the chosen point, or focus it in the drawing and use arrows (¼ unit), Shift+arrow (1 unit), Home (origin). Scale stays fixed while dragging and adjusts on release.
The drawing and decimals are approximate. Fractions and comparison with R are exact; irrational radicals may remain unsimplified. Only the principal-argument arc is drawn: k changes the written angle, not the point.
Formula, substitution and steps
Convention: Arg(z) ∈ (−π,π], or (−180°,180°]. Counterclockwise is positive. Zero has no argument.