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What is the geometric effect of T(z) = z + (4 - 2i)?

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Answer:

The geometric effect of a complex function can be understood by considering how it transforms points in the complex plane. In the case of the function T(z) = z + (4 - 2i), it represents a translation of the complex plane by adding the complex number (4 - 2i) to each point.

Explanation:

  • Geometrically, this means that every point in the complex plane is shifted horizontally by 4 units to the right and vertically by 2 units downwards. In other words, the entire complex plane is shifted in a specific direction.
  • To visualize this transformation, you can plot a grid of points in the complex plane and apply the transformation T(z) to each point. This will give you a new set of points that represent the transformed complex plane.
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