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:

Black Spruce

A species of tree in the pine family, native to northern parts of North America, characterized by its dark, dense foliage and adaptation to cold climates.

White Spruce

A species of spruce native to the northern temperate and boreal forests in North America, known for its use in construction and as Christmas trees.

Tamarack Trees

Deciduous conifers known for their ability to grow in cold, swampy conditions, distinct for shedding their needles in the winter.

Tropical Rain Forests

Densely forested regions located near the equator, characterized by high biodiversity, significant rainfall, and a warm climate year-round.