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Chapter 2: Problem 70

A stand-up comedian uses algebra in some jokes, including one about a telephone recording that announces "You have just reached an imaginary number. Please multiply by \(i\) and dial again." Explain the joke.

Short Answer

Expert verified
The joke plays on the concept of complex mathematics where 'i' is an imaginary unit. Converting an imaginary number to a real number involves multiplying by 'i'. This same concept is humorously applied to the situation of dialing an imaginary phone number.

Step by step solution

01

Understanding The Concept Of 'i'

The imaginary unit 'i' is a mathematical concept which is defined as having the property that \(i^2 = -1\). Thus, the square root of -1 is represented by 'i'.
02

Imaginary Numbers

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i'. For instance, \(2i\) where '2' is the real part and \(2i\) is the imaginary number.
03

Practical Application In The Joke

In real life, phone numbers are real numbers. The joke is that instead of dialing a real number, an imaginary number is reached. The message then instructs to multiply by 'i', which, in a mathematical sense, would transition the caller from 'imaginary' back to 'real'.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The inequality \(\frac{x-2}{x+3}<2\) can be solved by multiplying both sides by \((x+3)^{2}, x \neq-3,\) resulting in the equivalent inequality \((x-2)(x+3)<2(x+3)^{2}\).

Find the horizontal asymptote, if there is one, of the graph of rational function. $$h(x)=\frac{15 x^{3}}{3 x^{2}+1}$$

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$h(x)=\frac{1}{x}+1$$

Use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$(x-2)^{2}>0$$

The equation for \(f\) is given by the simplified expression that results after performing the indicated operation. Write the equation for \(f\) and then graph the function. $$\frac{x}{2 x+6}-\frac{9}{x^{2}-9}$$
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