STEMviz
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Complex Plane Sandbox

Plot complex numbers on the Argand (imaginary) plane, explore operations, roots and powers, and colour the plane by a function f(z).

Points

A point can use the points above it, e.g. c = ab. Drag any point that uses no other point; its field then reads a + bi.

  • reads asei⋅π3{ e}^{\frac{ i\cdot\pi}{3}}

    = 0.5 + 0.866i

  • reads asa⋅b a\cdot b

    = 0.134 + 2.232i

Selected point

a
Cartesian
a=2+ia = 2 + i
Modulus
∣a∣=2.23607|a| = 2.23607
Argument
0.46365 rad=26.565∘0.46365\,\text{rad} = 26.565^\circ
Exponential
a=2.23607 e0.46365 ia = 2.23607\,e^{0.46365\,i}
Conjugate
a‾=2−i\overline{a} = 2 - i

Principal argument: −π < θ ≤ π.

n
n = 3

Draw the roots or the powers of the selected point.

Function

reads asz3−1z2+1\frac{{ z}^{3}-1}{{ z}^{2}+1}

hue = arg⁡f(z)\arg f(z)brightness bands = ∣f(z)∣|f(z)|

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