Question

Identify the number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions may apply.) 3+i ​

Answer 1

Answer:

$z = 3 + i$ is complex as $a,b\in \mathbb{R}$, $b \neq 0$.

Step-by-step explanation:

A complex number comprehends all numbers of the form:

$z = a+i\cdot b$, $\forall \,a,b\in \mathbb{R}$

Where $i = \sqrt{-1}$.

In other words, complex numbers are an extension of real numbers.

There is the following classification depending on what values of $a$ and $b$ exist:

Real - $a \in \mathbb{R}$, $b = 0$

Complex - $a,b\in \mathbb{R}$, $b \neq 0$  

Pure imaginary - $a = 0$, $b \neq 0$ (The term "nonreal complex" is a synonym for pure imaginary complex)

Let be $z = 3 + i$, which is complex as $a,b\in \mathbb{R}$, $b \neq 0$.

Answer 2

The number contains both real and imaginary parts, hence it is classified as a complex number.

Complex numbers

Complex numbers are square roots of negative numbers. They are represented using the letter "i".

Complex number is expressed as z = x + iy where:

• x is the real part
• y is the imaginary part.

Given the value 3+i, since the number contains both real and imaginary parts, hence it is classified as a complex number.

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