Complex Numbers
Author: Roger Tobin

Drag point Z in the complex plane. The value is displayed at the top in both Re/Im and polar (r/theta) notation. Use checkboxes to display the complex conjugate Z* and/or the real and imaginary components.

ϕ

Show complex conjugate

Show real and imaginary parts

Re(z)

Im(z)

z = (2.6, 3.44)
ϕ0: atan(y(z) / x(z)) / π
r: sqrt(x(z)^(2) + y(z)^(2))
A = Intersect(xAxis, yAxis)
B: (r / 2, 0)
u = Vector(A, z)
C = Point(u)
c = CircleSector(A, B, C)
z' = Mirror(z, xAxis)
text3: "z = " * r * "ℯ"
ϕ = If(x(z) ≥ 0, If[y(z) > 0, ϕ0, ϕ0 + 2], ϕ0 + 1)
text4: "ί(" + ϕ + ")π"
d = Circle(A, z)
D = Point(d)
a = false
v = Vector(A, z')
z_1 = (2.56, 5.2)
r_1: sqrt(x(z_1)^(2) + y(z_1)^(2))
ϕ_1: atan(y(z_1) / x(z_1)) / π
text2_1: "z = " + (x(z_1)) + "+" + (y(z_1)) + "ί"
text2: "z* = " + (x(z)) + "-" + (y(z)) + "ί"
text5: "z* = " * r * "ℯ"
text6: "-ί (" + ϕ + ")π"
b = false
Rez: (x(z), 0)
Imz: (0, y(z))
w = Vector(A, Rez)
e = Vector(A, Imz)
f = Segment(Imz, z)
g = Segment(Rez, z)
Imz': (0, -y(z))
h = Vector(A, Imz')
i = Segment(Imz', z')
j = Segment(Rez, z')