Complex numbers are a set of numbers that include real numbers and imaginary numbers. They are
expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit,
defined as the square root of -1 (i = √-1). The 'a' part is the real part, and 'b' is the
imaginary part. 
Key aspects of complex numbers:
Real and Imaginary Parts: A complex number has
both a real part (a) and an imaginary part (bi). 
Imaginary Unit: The imaginary unit 'i' is crucial
for defining complex numbers. It allows us to work with the square roots of negative numbers.

Representation: Complex numbers are often represented in the form a + bi, also known as the
rectangular or standard form. 
Set Notation: The set of all complex numbers is denoted by the
symbol ℂ (or sometimes C). 
Conjugate: The complex conjugate of a + bi is a - bi. 
Operations:
Complex numbers can be added, subtracted, multiplied, and divided, following specific rules.

Examples:
5 + 2i is a complex number with a real part of 5 and an imaginary part of 2i. 
3i is a
purely imaginary number (real part is 0). 
7 can be written as a complex number 7 + 0i. 
-4 - 5i
is a complex number with a real part of -4 and an imaginary part of -5i. 
Applications:
Complex
numbers are used in various fields, including:
Physics: Quantum mechanics, electromagnetism, and
fluid dynamics.
Engineering: Electrical engineering and signal processing.
Mathematics: Number
theory, geometry, and analysis.