Let $\mathrm { z } _ { 1 } = \mathrm { r } _ { 1 } \left( \cos \theta _ { 1 } + \mathrm { i } \sin \theta _ { 1 } \right)$

question 120

Essay

Let $\mathrm { z } _ { 1 } = \mathrm { r } _ { 1 } \left( \cos \theta _ { 1 } + \mathrm { i } \sin \theta _ { 1 } \right)$ and $\mathrm { z } _ { 2 } = \mathrm { r } _ { 2 } \left( \cos \theta _ { 2 } + \mathrm { i } \sin \theta _ { 2 } \right) , \mathrm { r } _ { 2 } \neq 0$ . Verify that $\mathrm { z } _ { 1 } / \mathrm { z } _ { 2 } = \mathrm { r } _ { 1 } / \mathrm { r } _ { 2 } \left[ \cos \left( \theta _ { 1 } - \theta _ { 2 } \right) + \mathrm { i } \sin \left( \theta _ { 1 } - \theta _ { 2 } \right) \right]$ .

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Definitions:

Federal Reserve System

The central banking system of the United States, regulating the national money supply and aiming to maintain economic stability.

Monopoly Power

The ability of a single seller to influence the price of goods or services in a market.

Commodity Money

Money whose value comes from a commodity out of which it is made, such as gold and silver, which inherently have value.

Goldsmith

A craftsperson skilled in making items of gold.