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) \(4 ( .7660 + .6428 \mathrm { i } ) , 4 ( - .9397 + .3420 \mathrm { i } ) , 4 ( .1736 - .9848 \mathrm { i } )\)

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Definitions:

Seating Capacity

The maximum number of individuals that can be accommodated in a venue with available seats.

Monopoly Profits

Excess profits earned by a monopoly as a result of having exclusive control over a market and the ability to set higher prices.

Profit-Maximizing

The method or plan of altering manufacturing and sales activities to maximize profit.

Marginal Cost

The expense incurred from manufacturing an extra single unit of a service or product.