Definitions for imaginary part
imag·i·nary part

Princeton's WordNetRate this definition:0.0 / 0 votes

1. imaginary part, imaginary part of a complex numbernoun

   the part of a complex number that has the square root of -1 as a factor

WiktionaryRate this definition:0.0 / 0 votes

1. imaginary partnoun

   Of a complex number a + bi, the value b.

WikipediaRate this definition:0.0 / 0 votes

1. imaginary part

   In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation i 2 = − 1 {\displaystyle i^{2}=-1} ; every complex number can be expressed in the form a + b i {\displaystyle a+bi} , where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number a + b i {\displaystyle a+bi} , a is called the real part, and b is called the imaginary part. The set of complex numbers is denoted by either of the symbols C {\displaystyle \mathbb {C} } or C. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world.Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficients has a solution which is a complex number. For example, the equation ( x + 1 ) 2 = − 9 {\displaystyle (x+1)^{2}=-9} has no real solution, since the square of a real number cannot be negative, but has the two nonreal complex solutions − 1 + 3 i {\displaystyle -1+3i} and − 1 − 3 i {\displaystyle -1-3i} . Addition, subtraction and multiplication of complex numbers can be naturally defined by using the rule i 2 = − 1 {\displaystyle i^{2}=-1} combined with the associative, commutative, and distributive laws. Every nonzero complex number has a multiplicative inverse. This makes the complex numbers a field that has the real numbers as a subfield. The complex numbers also form a real vector space of dimension two, with {1, i} as a standard basis. This standard basis makes the complex numbers a Cartesian plane, called the complex plane. This allows a geometric interpretation of the complex numbers and their operations, and conversely expressing in terms of complex numbers some geometric properties and constructions. For example, the real numbers form the real line which is identified to the horizontal axis of the complex plane. The complex numbers of absolute value one form the unit circle. The addition of a complex number is a translation in the complex plane, and the multiplication by a complex number is a similarity centered at the origin. The complex conjugation is the reflection symmetry with respect to the real axis. The complex absolute value is a Euclidean norm. In summary, the complex numbers form a rich structure that is simultaneously an algebraically closed field, a commutative algebra over the reals, and a Euclidean vector space of dimension two.

ChatGPTRate this definition:0.0 / 0 votes

1. imaginary part

   The imaginary part is a component of a complex number which is expressed as a real number multiplied by the imaginary unit "i" (in some contexts "j" is used instead of "i"). It's called 'imaginary' because it exists on a different dimension than the 'real' part of the complex number. In a complex number of the form a + bi, where a and b are real numbers, 'b' would be the imaginary part.

Matched Categories

1. • Pure Imaginary Number

How to pronounce imaginary part?

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Numerology

1. Chaldean Numerology

   The numerical value of imaginary part in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of imaginary part in Pythagorean Numerology is: 8

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=imaginary part
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Imaginary_Part
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Imaginary_Part
4. ^ ChatGPT
   https://chat.openai.com