Chapter 3 Complex Numbers
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Project on Complex Numbers
In mathematics, complex numbers are numbers of the form \( a
+ bi \), where \( a \) and \( b \) are real numbers, and \( i \) is the
imaginary unit, defined as \( i^2 = -1 \). In this expression, \( a \) is
called the real part, and \( b \) is called the imaginary part.
Complex numbers extend the concept of real numbers to
include solutions to equations that have no real solutions. They are used
extensively in various branches of mathematics, including algebra, calculus,
and physics.
One key property of complex numbers is that they can be represented
geometrically on the complex plane, where the real part corresponds to the
horizontal axis and the imaginary part corresponds to the vertical axis. This
representation allows for operations such as addition, subtraction,
multiplication, and division to be visualized as geometric transformations on
the complex plane.
Complex numbers also have applications in various fields, such as electrical engineering, signal processing, and quantum mechanics, where they are used to model phenomena involving oscillations, waves, and quantum states.