Chapter 2.4, Problem 2E

To determine

To fill the blank to complete the given statement:

“An $\underset{\_}{}$ number has the form $a+bi$ , where $a\ne 0,b\ne 0$ ”

Answer to Problem 2E

“An $\underset{\_}{\text{ imaginary }}$ number has the form $a+bi$ , where $a\ne 0,b\ne 0$ .”

Explanation of Solution

Given:

The given statement is

“An $\underset{\_}{}$ number has the form $a+bi$ , where $a\ne 0,b\ne 0$ .”

Concept Used:

The standard form of a complex number is $a+bi$ , where a, and b are real numbers.

• When $b=0$ , the number $a+bi$ is a real number.
• When $b\ne 0$ , the number $a+bi$ is an imaginary number. A number of the form $bi$ , where $b\ne 0$, is a pure imaginary number.

Calculation:

To fill the blank to complete the given statement use the definition of standard form of a complex number and real number.

The standard form of a complex number is $a+bi$ , where a, and b are real numbers. And when $a\ne 0,b\ne 0$ the number $a+bi$ is an imaginary number.

Thus, the blank of given statement is filled by: “imaginary”.

“An $\underset{\_}{\text{ imaginary }}$ number has the form $a+bi$ , where $a\ne 0,b\ne 0$ .”