2) Give an example of a real number, an imaginary number, and a complex number. (3 points)(3 points) Real number: Imaginary number: Complex number: Question 2 3) Explain how you know what type of number each one is.

Answer 1

Real number: \( 5 \)
Imaginary number: \( 3i \)
Complex number: \( 2 + 4i \)

Explanation:

1. Real Number: \( 5 \)
   A real number is any number that can be found on the number line. This includes all the positive and negative integers, fractions, and irrational numbers. The number \( 5 \) is a whole number and does not involve any imaginary unit.

2. Imaginary Number: \( 3i \)
   An imaginary number is a number that can be expressed as a real number multiplied by the imaginary unit \( i \), where \( i = \sqrt{-1} \). The number \( 3i \) is purely imaginary because it has no real part (the real part is zero), and it is expressed entirely as a multiple of \( i \).

3. Complex Number: \( 2 + 4i \)
   A complex number is a number that has both a real part and an imaginary part and is usually expressed in the form \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part. The number \( 2 + 4i \) has a real part (2) and an imaginary part (4i), making it a complex number.