Loci in the Argand Diagram

locus

half-line: arg(z-

z

1

) = θ

θ

0

r

1.5

k

1

c

3

α

1.57

x

1

1

y

1

0

x

2

2

y

2

1

This Demonstration shows loci (in blue) in the Argand diagram, which should normally be recognized from their equations by high school students in certain countries. Five equations are demonstrated, each containing a constant that can be varied using the corresponding controller. The constant complex numbers

z

1

and

z

2

(represented by red points) are set by choosing values of

x

1

,

y

1

,

x

2

, and

y

2

.