Question

classify the following numbers as complex, imaginary, or real: option #1: complex option #2: imaginary option #3: real (2 points) $sqrt{3}$ is a number as shown in option #. $5i$ is a number as shown in option #. $3 + 5i$ is a number as shown in option #.

Explanation:

Step1: Recall number - type definitions

A real number is a number that can be found on the number line. An imaginary number is of the form $bi$ where $b$ is a non - zero real number and $i=\sqrt{- 1}$. A complex number is of the form $a + bi$ where $a$ and $b$ are real numbers.

Step2: Classify $\sqrt{3}$

$\sqrt{3}\approx1.732$ is a non - negative square root and can be located on the real number line. So it is a real number.

Step3: Classify $5i$

Since it is of the form $bi$ with $b = 5
eq0$, it is an imaginary number.

Step4: Classify $3 + 5i$

It is of the form $a+bi$ where $a = 3$ and $b = 5$, so it is a complex number.

Answer:

$\sqrt{3}$ is a number as shown in Option #3.
$5i$ is a number as shown in Option #2.
$3 + 5i$ is a number as shown in Option #1.