Which of the Following Is a Fourth Root Of $1 ?$

question 88

Multiple Choice

Which of the following is a fourth root of $1 ?$
I. $\cos \left( \frac { 3 \pi } { 2 } \right) + i \sin \left( \frac { 3 \pi } { 2 } \right)$
II. $\frac { 1 } { 4 } ( \cos ( 0 ) + i \sin ( 0 ) )$
III. $\cos \left( \frac { \pi } { 4 } \right) + i \sin \left( \frac { \pi } { 4 } \right)$

• A) None are roots.
• B) II and III are the only roots.
• C) I and II are the only roots.
• D) I, II, and III are roots.
• E) I is the only root.

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Definitions:

Efficiency Loss

The loss of economic efficiency that can occur when the equilibrium for a good or a service is not achieved or is unattainable.

Tax

Compulsory financial obligation or different form of levy placed on a taxpayer by a government entity to finance public spending.

Excise Tax

A tax imposed on specific goods, services, or activities within a country, often levied on items like tobacco, alcohol, and gasoline to discourage their use or generate revenue.

Deadweight Losses

Economic inefficiencies that occur when the equilibrium in a market is not achieved or is distorted, typically resulting in lost welfare or inefficiency.