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Dilation
A dilation, also referred to as a homothety, is a specific type of geometric transformation that enlarges or shrinks objects while preserving their shape. In the context of complex analysis, a dilation can be thought of as a transformation that scales the size of a figure in the complex plane by a fixed factor and may change its orientation.
A dilation in the complex plane can be defined by a complex function of the form:
Here,
When
In summary, a dilation is a geometric transformation that scales the size of a figure in the complex plane by a fixed factor, preserves its shape, and may change its orientation, depending on the argument of the dilation factor.