The Basics of Complex Numbers
Concept

Complex Numbers

The set of complex numbers, represented by the symbol C, is formed by all numbers that can be written in the form z=a+bi, where a and b are real numbers and i is the imaginary unit. Here, a is called the real part and b is called the imaginary part of the complex number.
Breakdown of a complex number z=a+bi where a is the real part and b is the imaginary part; Re(z)=a, Im(z)=b.
If b≠ 0, the number is an imaginary number. Conversely, if b=0, the number is real. Additionally, if a=0 and b≠ 0, the number is a pure imaginary number. Both real and imaginary numbers are subsets of the complex number set.
A big set divided into two parts. The left-hand part is the Real Numbers set; the right-hand part is the Imaginary Numbers set; inside the Imaginary Numbers set, there is a small set labeled as the Pure Imaginary Numbers set.
Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.


a+bi = c+di ⇔ a=c and b=d

Exercises