Chapter 2.4, Problem 1E

To determine

To match the complex number with its definition.

Answer to Problem 1E

  $\begin{array}{l}\text{a)}\text{Real number}\to \left(ii\right)a+bi,b=0\\ \text{b)}\text{Imaginary number}\to \left(iii\right)a+bi,a\ne 0,b\ne 0\\ \text{c) Pure imaginary number}\to \left(i\right)a+bi,a=0,b\ne 0\end{array}$

Explanation of Solution

Given:

Real number

i) $a+bi,a=0,b\ne 0$

Imaginary number

ii) $a+bi,b=0$

Pure imaginary number

iii) $a+bi,a\ne 0,b\ne 0$

An imaginary number consists of real part and imaginary part. The standard form an imaginary number is $a+bi$ , where a is real part and $bi$ is imaginary part.

If the value of b is 0, then only the real part is a is left and the number becomes real number. If the real part is 0, that $a=0$ , then only imaginary part is left and the number is called pure imaginary number.

Thus, the correct match can be given as follows:

  $\begin{array}{l}\text{a)}\text{Real number}\to \left(ii\right)a+bi,b=0\\ \text{b)}\text{Imaginary number}\to \left(iii\right)a+bi,a\ne 0,b\ne 0\\ \text{c) Pure imaginary number}\to \left(i\right)a+bi,a=0,b\ne 0\end{array}$