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

question 46

Multiple Choice

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

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

---

Definitions:

Industrial Organization

A field of economics that studies the structure of and boundaries between firms and markets, and the strategic interactions within them.

Subsidize Tobacco Production

Financial support provided by governments to farmers or companies to assist in the growing or manufacturing of tobacco products.

Global Warming

The long-term rise in Earth's average surface temperature, largely due to human activities that emit greenhouse gases into the atmosphere.

Interest Rate

The percentage at which interest is paid by a borrower for the use of money that they borrow from a lender.