Find All Cube Roots of the Complex Number $- 125 \mathrm { i }$

question 383

Multiple Choice

Find all cube roots of the complex number. Leave answers in trigonometric form.
- $- 125 \mathrm { i }$

• A) \(5 \operatorname { cis } ^ { \circ } 210,5 \operatorname { cis } 270 ^ { \circ } , 5 \operatorname { cis } 330 ^ { \circ }\)
• B) \(5 \operatorname { cis } 30 ^ { \circ } , 5 \operatorname { cis } ^ { \circ } 60,5 \operatorname { cis } 90 ^ { \circ }\)
• C) \(5 \operatorname { cis } 90 ^ { \circ } , 5 \operatorname { cis } ^ { \circ } 180,5 \operatorname { cis } 270 ^ { \circ }\)
• D) \(5 \operatorname { cis } 90 ^ { \circ } , 5 \operatorname { cis } ^ { \circ } 210,5 \operatorname { cis } 330 ^ { \circ }\)

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Definitions:

Expansionary Gap

An economic situation where the actual output exceeds the potential output, often leading to inflation.

Nominal Value of Output

The gross value of all goods and services produced, measured using current prices without adjusting for inflation.

Money Supply

The total amount of monetary assets available in an economy, including cash and deposits.

Price Level

The total economy’s current average pricing for goods and services produced.