Problem 68 - College Algebra

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The word imaginary in imaginary numbers tells me that these numbers are undefined.

Step-by-Step Solution

Answer

The statement 'The word imaginary in imaginary numbers tells me that these numbers are undefined' does not make sense. Imaginary numbers are defined as multiples of the square root of -1, not as undefined entities.

Step 1: Understanding Imaginary Numbers

Imaginary numbers are actually very well-defined. The term 'imaginary' is used because these numbers are multiples of the square root of -1, referred to as 'i'. You can write any imaginary number as 'bi', where 'b' is a real number.

Step 2: Evaluating the statement

Given the proper definition of imaginary numbers, the statement 'The word imaginary in imaginary numbers tells me that these numbers are undefined.' is not correct. This is due to the fact that while these numbers may not have a real counterpart, they are by no means undefined. They have a well-established definition within the field of mathematics.