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PcumP_Ravenclaw
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Rotation isometry on the complex plane refers to a transformation that preserves distances and angles between points on the complex plane. This means that the shape and size of figures remain unchanged after the transformation is applied.
Rotation isometry is a specific type of isometry that involves rotating the complex plane around a fixed point. Other types of isometry include translation, which involves shifting the complex plane, and reflection, which involves flipping the complex plane over a line.
If a function is a rotation isometry, it means that it is a one-to-one and onto mapping from the complex plane to itself that preserves distances and angles. This means that the function can be represented as a complex number raised to a power, where the absolute value of the complex number is equal to the scale factor and the argument is equal to the angle of rotation.
To determine if a transformation is a rotation isometry, you can use the following criteria:
Rotation isometry on the complex plane has many practical applications, including: