Complex numbers · demo

Determine and use conjugates

Drag z. Its conjugate z̄ reflects across the real axis. Toggle the product — z·z̄ is always the real number |z|².

z z̄

Drag z · scroll to zoom · drag background to pan

The numbers

Show product z · z̄
always a non-negative real
Show |z| circle
z and its conjugate both lie on this circle

Working