imaginary numbers
Roots of negatives
Imaginary numbers are numbers that, when squared, produce a negative result—something impossible with ordinary numbers.
The basic unit is *i*, defined as the square root of negative one.
Despite the name, imaginary numbers have practical applications in engineering, physics, and signal processing.
Combined with real numbers, they form complex numbers: 3 + 2i.
Coordinate system for imaginaries
- Cartesian planeTwo-dimensional plotting surface
- magnitudeSize or scale
- phaseDistinct period in sequence
- conjugateModify verbs grammatically
Study of circuits and power
- impedanceAC circuit opposition
- signal processingMathematical manipulation of waveforms
- quantum mechanicsPhysics at nanoscopic scales
- control systemsMechanisms maintaining desired outputs
wave function · resonance · oscillation · Schrödinger equation · fluid dynamics · fractals
Polynomial of degree two
- rootsUnderground nutrient absorbers
- polynomialExpression with variable terms
- coefficientsNumerical multipliers in expressions
- discriminantFormula determining root nature
quadratic formula · binomial · radical · factoring · irrational · completing the square
Hypercomplex number with four components
- HamiltonFirst Treasury secretary
- higher dimensionsSpaces with four-plus axes
- Clifford algebraAlgebra from quadratic forms
Demonstration of truth
- theoremDemonstrated logical conclusion
- axiomSelf-evident starting principle
- definitionStatement of meaning
- abstractionDistilling to essential qualities
formalism · field · closure · existence · construction · consistency · Cardano · historical development
complex plane
Coordinate system for imaginaries
- Cartesian planeTwo-dimensional plotting surface
- magnitudeSize or scale
- phaseDistinct period in sequence
conjugate · modulus · argument · Euler's formula · absolute value
electrical engineering
Study of circuits and power
- impedanceAC circuit opposition
- signal processingMathematical manipulation of waveforms
- quantum mechanicsPhysics at nanoscopic scales
control systems · wave function · resonance · oscillation · Schrödinger equation · fluid dynamics · fractals
quadratic equation
Polynomial of degree two
- rootsUnderground nutrient absorbers
- polynomialExpression with variable terms
- coefficientsNumerical multipliers in expressions
discriminant · quadratic formula · binomial · radical · factoring · irrational · completing the square
quaternion
Hypercomplex number with four components
- HamiltonFirst Treasury secretary
- higher dimensionsSpaces with four-plus axes
- Clifford algebraAlgebra from quadratic forms
proof
Demonstration of truth
- theoremDemonstrated logical conclusion
- axiomSelf-evident starting principle
- definitionStatement of meaning
abstraction · formalism · field · closure · existence · construction · consistency · Cardano · historical development
- mathematicsalgebra, arithmetic, calculus, geometry, addition
- math conceptsangle, algebra, circle, equations, equation
- number typesintegers, fractions, decimals, primes, evens
- Math Worldalgebra, calculus, geometry, equations, proofs
- complex analysismodulus, complex plane, analytic, singularity, pole
- Hypercomplex Mathquaternion, Clifford algebra, rotor, rotors, blade
imaginary numbersreal numbers
Complete ordered field
real · reals · rational numbers · natural numbers · counting numbers
imaginary, number, imagine, image, imagination, imaginative, imaginatively, imagined, imaging