Geometric Demonstration of Complex Subtraction z1 - z2 = z3
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This GeoGebra example visually demonstrates the geometric meaning of complex subtraction: given two complex numbers z1 and z2, their difference z3 = z1 - z2 corresponds to a vector in the complex plane, and z1, z2, z3 form a triangle relationship. The core mathematical concepts include the consistency between complex subtraction and vector subtraction, as well as the application of similar triangles in complex geometry. Construction highlights: the Segment command is used to create line segments, and the Angle command marks angles; objects include z_1, z_2, z_3, a, α, b, c, and text1, which together illustrate the subtraction result through segments and angles. This is suitable for high school or early college students learning complex numbers and vectors, and also for teachers to use in classroom demonstrations to foster an intuitive understanding of complex subtraction.
GeoGebra Commands & Parameters
Segment((0, 0), z_1) → aAngle(xAxis, a) → αSegment((0, 0), z_2) → bSegment((0, 0), z_3) → c