Find All the Complex Roots $- 8 \mathrm { i }$

question 3

Multiple Choice

Find all the complex roots. Leave your answers in polar form with the argument in degrees.
-The complex cube roots of $- 8 \mathrm { i }$

• A) \(2 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) , 2 \left( \cos 210 ^ { \circ } + i \sin 210 ^ { \circ } \right) , 2 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)\)
• B) \(512 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) , 512 \left( \cos 210 ^ { \circ } + i \sin 210 ^ { \circ } \right) , 512 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)\)
• C) \(8 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) , 8 \left( \cos 210 ^ { \circ } + i \sin 210 ^ { \circ } \right) , 8 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)\)
• D) \(2 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right) , 2 \left( \cos 300 ^ { \circ } + i \sin 300 ^ { \circ } \right) , 2 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)\)

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Definitions:

Uniformitarianism

The geological principle suggesting that the same processes and natural laws that operate in the universe now have always operated in the past.

Natural Selection

A fundamental mechanism of evolution, where organisms better adapted to their environment tend to survive and produce more offspring.

Catastrophism

The theory that the Earth has been shaped by sudden, short-lived, violent events, possibly worldwide in scope, contrasting with uniformitarianism which emphasizes gradual changes.

Mitosis

A kind of cell division that produces new cells having exactly the same number of chromosome pairs, and hence copies of genes, as the parent cell.