A complex number is an expression of the form a + bi, where a and b are real numbers, and i is an abstract symbol, the so-called imaginary unit, whose meaning will be explained … See more

While the above low-level definitions, including the addition and multiplication, accurately describes the complex numbers, there are other, equivalent approaches that reveal the abstract algebraic structure of the complex numbers more … See more

Complex numbers have applications in many scientific areas, including signal processing, control theory, electromagnetism See more

• Analytic continuation
• Circular motion using complex numbers
• Complex-base system
• Complex coordinate space
• Complex geometry See more

The solution in radicals (without trigonometric functions) of a general cubic equation, when all three of its roots are real numbers, contains the square roots of negative numbers, … See more

The study of functions of a complex variable is known as complex analysis and has enormous practical use in applied mathematics as well as in other branches of mathematics. … See more

Algebraic characterization
The field $${\displaystyle \mathbb {C} }$$ has the following three properties:
• First, … See more