We are asked to match each type of complex number with its definition. Let's start by simplifying the definitions.
Definition
Simplify
Simplified Definition
(i) a + bi, a = 0, b ≠0
0 + bi = bi
(i) bi, b≠0
(ii) a + bi, b= 0
a + 0i=a
(ii) a
(iii) a + bi, a ≠0, b ≠0
a + bi
(iii) a + bi, a ≠0, b ≠0
Recall that each complex number can be written in standard form a+bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of - 1. In this form, a is called the real part and bi is called the imaginary part.
Standard Form of a Complex Number [0.4em] a_(real part)+bi_(imaginary part)
A number is a real number if it is only the real part, a pure imaginary number if it is only the imaginary part, and an imaginary number if it has both parts. With this in mind, we can pair each type of complex number with its definition. Let's do it!
