COMPLEX PLANE Meaning and
Definition
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The complex plane, also known as the Argand plane or the Gaussian plane, is a mathematical construct that represents complex numbers graphically. It is a two-dimensional coordinate system consisting of a horizontal axis, known as the real axis, and a vertical axis, known as the imaginary axis. The complex plane allows for the representation of complex numbers in the form a + bi, where "a" represents the real part of the number and "b" represents the imaginary part.
In the complex plane, each point corresponds to a unique complex number. The real axis is aligned with the familiar number line, with positive numbers to the right and negative numbers to the left. The imaginary axis is perpendicular to the real axis, with positive numbers above and negative numbers below. The origin of the complex plane, where the real and imaginary axes intersect, represents the complex number 0.
The complex plane provides a geometric representation for complex arithmetic, making it easier to visualize and analyze complex numbers and operations. It allows for operations such as addition, subtraction, multiplication, and division to be represented as translations, rotations, and magnifications in the plane. It also provides a means to graphically illustrate relationships between complex numbers, such as the distance between two complex numbers or the angle they form with the origin.
Overall, the complex plane is an essential tool in complex analysis and allows for a graphical representation of complex numbers and their operations.
Common Misspellings for COMPLEX PLANE
- xomplex plane
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Etymology of COMPLEX PLANE
The term "complex plane" originated from the combination of the words "complex" and "plane".
The term "complex" is derived from the Latin word "complexus", which means "together" or "enfolded". It was initially introduced by the French mathematician and philosopher René Descartes in the 17th century to describe numbers involving both real and imaginary parts. Descartes introduced the concept of a "complex number" by representing it as an ordered pair of real numbers, where the first number is the real part and the second number is the imaginary part.
The term "plane" refers to a two-dimensional flat surface. In the context of mathematics, a plane is often used to represent the set of complex numbers. In this plane, the horizontal axis represents the real numbers, while the vertical axis represents the imaginary numbers. The combination of these axes forms a two-dimensional complex plane.
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