OBJECTIVE To examine statements about complex numbers and to decide if they are true or false
KEY TERM
A complex number z is a number that can be written in the form z = a + bi, where a, b ∈ R and i = √
___ −1 .
Examples of complex numbers z = 3 + 2i = 3 + 2 × i [a = 3 ∈ R, b = 2 ∈ R and i = √
z = − 1 _
z = −5 − 7i 2 + √
__ 3 i
[a = −5 ∈ R, b = −7 ∈ R and i = √
z = –7 = –7 + 0i z = – 4 i = 0 – 4 i z = 0 = 0 + 0 i
It is important to note the following: 1. a and b can be any real numbers. 2. a is called the real part (Re) of the complex number.
___ −1 ]
___ −1 ]
Real numbers such as 2 and imaginary numbers such as 2i exist, but can a number be both real and imaginary at the same time? This question leads to the idea of a complex number.
