Give a Geometric Interpretation of What Happens to a Complex

question 287

Essay

Give a geometric interpretation of what happens to a complex number when it is squared. Describe what
happens to the argument and to the distance from the origin. Will the distance from the origin increase,
decrease, or remain the same?

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Definitions:

Sternum

A flat bone located in the center of the chest, connected to the ribs via cartilage, forming a major part of the rib cage and protecting vital organs in the thorax.

Mandibular Fossa

A depression in the temporal bone that forms the socket for the condylar process of the mandible, contributing to the temporomandibular joint.

Temporal

Related to time or also pertaining to the temples of the head near the temporal bones of the skull.

Sphenoid

A butterfly-shaped bone at the base of the skull, behind the eyes, touching on various important structures and enclosing the pituitary gland.