Find All Cube Roots of the Complex Number $64 \operatorname { cis } 120 ^ { \circ }$

question 194

Multiple Choice

Find all cube roots of the complex number. Leave answers in trigonometric form.
- $64 \operatorname { cis } 120 ^ { \circ }$

• A) \(4 ( .6428 + .7660 \mathrm { i } ) , 4 ( - .3420 + .9397 \mathrm { i } ) , 4 ( .9848 - .1736 \mathrm { i } )\)
• B) \(4 \left( - \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right)\), \(4 \left( \frac { 1 } { 2 } \mathrm { i } - \frac { \sqrt { 3 } } { 2 } \right) , 4 \left( \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right)\)
• C) \(4 \left( \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \mathrm { i } \right) , 4 \left( - \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \mathrm { i } \right) , 4 \left( \frac { \sqrt { 3 } } { 2 } - \frac { 1 } { 2 } \mathrm { i } \right)\)
• D) \(4 ( .7660 + .6428 \mathrm { i } ) , 4 ( - .9397 + .3420 \mathrm { i } ) , 4 ( .1736 - .9848 \mathrm { i } )\)

Understand the roles and sources of different hormones within the human body.

Compare the response times and effects of the endocrine and nervous systems.

Identify the mechanisms through which hormones exert their effects, including second messengers.

Describe the concept of feedback loops in hormone regulation.

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Definitions:

Water Uptake

The process by which plants absorb water from the soil through their roots to maintain vital functions.

Alternate

To occur or happen in succession; to switch between two or more states, actions, or conditions.

Leaf Arrangement

The pattern or configuration of leaves on the stem of a plant, which can be alternate, opposite, or whorled, among others.

Node

A point along a stem or branch at which leaves, branches, or flowers originate; in networks, a node is a junction or connection point.