College Algebra & Trigonometry, 2018a

40 CHAPTER 1. ALGEBRA REVIEW
devised a system in which all complex numbers are a combination of a Real part
(a) and an ”imaginary” part (bi).
The complex numbers are a two dimensional number system represented by the
double barred C: C = {a + bi : a, b ∈ R}, where i is the complex unit defined
as i = √ −1. Throughout the late 1700’s and early 1800’s mathematicians gradually
moved towards a geometrical interpretation of the two-dimensional complex
numbers. What is today known as the ”Argand diagram” represents the real valued
portion of a complex number along a horizontal axis and the multiple of the
complex unit along the vertical axis.
Im
5i
−1+4i
4i
3i
2i
3+2i
1i
R
−5 −4 −3 −2 −1 1 2 3 4 5
−1i
−2i
−3i
−4i
−5i