Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.1 - Complex Numbers - Exercise Set - Page 315: 69


See the explanations below.

Work Step by Step

Consider, Joke 1: If you divide $6$, $973$ by $0$, you die. The division of $6$ by $0$ is such that it gives an undefined value. \[\frac{6}{0}=\infty \] The division of $973$ by $0$ is such that it gives an undefined value. \[\frac{973}{0}=\infty \] Joke 1 describes that, no matter how many times the number is divided by $0$, the result will always be undefined or not known. Joke 2: Once, this guy tried to find the square root of $-9$, and his eyeballs turned black. The square root of $-9$ is $\sqrt{-9}$ and its value is not a real number but an imaginary number. The imaginary value of $\sqrt{-9}$ is, $\begin{align} & \sqrt{-9}=\sqrt{\left( -1 \right)\left( 9 \right)} \\ & =\sqrt{-1}\cdot \sqrt{9} \\ & =i\sqrt{9} \end{align}$ Where, $i$ is an imaginary unit. Joke 2 describes that the value of a square root of a negative number $-9$ is not real but an imaginary number. Joke 3: This girl my brother knows found out exactly what $\text{ }\!\!\pi\!\!\text{ }$ equals but she went nuts. The number $\text{ }\!\!\pi\!\!\text{ }$ is a Greek letter and is a mathematical constant. Its value is approximately equal to $3.14159$, however it has an infinite number of digits, so finding out its "true" value would be impossible.
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