Multiplication of complex numbers
We can get the result of multiplying two complex numbers adding their arguments and multiplying their modules.
Then multiplication of z1 by z2 is a dilative rotation with center at the origin, the angle of the rotation is the argument of z2 and the dilatation ratio is the modulus of z2.
In this representation we want to show the dilative rotation using an animation. The result is the blue dot.
We can drag the orange dots.
REFERENCES
Klein - Elementary Mathematics from an Advanced Standpoint (Arithmethic, Algebra, Analysis). Ed. Dover.(pag. 57)
LINKS
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The product as a complex plane transformation
The multiplication by a complex number is a transformation of the complex plane: dilative rotation.
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Dilative rotation
A Dilative Rotation is a combination of a rotation an a dilatation from the same point.
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Equiangular spiral
In an equiangular spiral the angle between the position vector and the tangent is constant.
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