contourHSC Mathematics Extension 2 · Loci · Mainstage

Where can z be?

Set a, b and θ. Then hover a point z: the two arguments get subtracted in front of you, and the locus is every z where that difference lands on θ.

abthe locusthe other arcz

Points

a =

b =

Real part on the left, imaginary part on the right. Or drag a and b on the diagram.

Angle θ

π/2

90°

Or type θ =π

Any value from −1 to 1 (a multiple of π). Press Enter to apply.

At the point z

z– arg(z − a)– arg(z − b)– difference–

Difference = θ, so z is on the locus.

Analysis

chord |a − b|– sin θ– radius– centre– arc– arc length–

Show

Show the other arc (difference = −θ) Show the full circle Show arg(z − a) and arg(z − b) at a and b

Presets

The difference is reduced to (−π, π]. The angle marked at z is the anticlockwise turn from the direction of z − b to the direction of z − a. On the other arc that turn is −θ, so those points are not on the locus.

Built for the Term 3 Holidays Workshop (Part II, loci). Scan the QR in your booklet to reopen this page.