complex numbers
Real plus imaginary
Complex numbers extend the real number system by including the imaginary unit *i*, defined as the square root of −1.
A complex number takes the form *a* + *bi*, where *a* and *b* are real numbers—*a* is the real part, *bi* the imaginary part.
They're essential in electrical engineering, quantum mechanics, and signal processing, where real numbers alone can't describe oscillations or rotations.
The equation has no real solutions, only complex numbers.
Modify verbs grammatically
- modulusAbsolute value operation
- argumentReasoned case or dispute
- Cartesian coordinatesPerpendicular-axis position notation
- polar coordinatesPoint location using angle, distance
Euler's formula · cis · ordered pair · absolute value · unit circle · bi · magnitude
Expression with variable terms
- equationMathematical equality assertion
- quadraticInvolving squared terms
- cubicOf three dimensions
- rootUnderground absorbing structure
factor · algebraic · coefficient · variable · quadratic formula · discriminant · factorization · eigenvalue
Quantum state's mathematical representation
- quantum mechanicsPhysics at nanoscopic scales
- Schrodinger equationQuantum state evolution law
- superpositionCoexisting in multiple states
- amplitudeMaximum oscillation displacement
phase · interference · electromagnetic wave · oscillation · AC voltage · quantum state · optics · diffraction
Mathematical manipulation of waveforms
- impedanceAC circuit opposition
- frequency responseOutput versus input frequencies
- control systemsMechanisms maintaining desired outputs
- resonanceAmplified oscillation at natural frequency
bandwidth · phase shift · amplitude · feedback · electrical engineering · telecommunications
Joining quantities mathematically
- subtractionRemoving quantities mathematically
- multiplicationProduct-finding operation
- divisionSplitting into parts
- exponentiationRaising to a power
Matter left behind
- singularityPoint where values explode
- poleCylindrical shaft or extremity
- harmonic functionLaplacian equals zero everywhere
conjugate
Modify verbs grammatically
- modulusAbsolute value operation
- argumentReasoned case or dispute
- Cartesian coordinatesPerpendicular-axis position notation
polar coordinates · Euler's formula · cis · ordered pair · absolute value · unit circle · bi · magnitude
polynomial
Expression with variable terms
root · factor · algebraic · coefficient · variable · quadratic formula · discriminant · factorization · eigenvalue · eigenvector
wavefunction
Quantum state's mathematical representation
- quantum mechanicsPhysics at nanoscopic scales
- Schrodinger equationQuantum state evolution law
- superpositionCoexisting in multiple states
amplitude · phase · interference · electromagnetic wave · oscillation · AC voltage · quantum state · optics · diffraction · polarization
signal processing
Mathematical manipulation of waveforms
- impedanceAC circuit opposition
- frequency responseOutput versus input frequencies
- control systemsMechanisms maintaining desired outputs
resonance · bandwidth · phase shift · amplitude · feedback · electrical engineering · telecommunications
addition
Joining quantities mathematically
- subtractionRemoving quantities mathematically
- multiplicationProduct-finding operation
- divisionSplitting into parts
residue
Matter left behind
- singularityPoint where values explode
- poleCylindrical shaft or extremity
- harmonic functionLaplacian equals zero everywhere
- hypercomplex numbersquaternion
- precalculusfunctions, polynomials, trigonometry, logarithms, exponential functions
- mathaddition, subtraction, multiplication, division, algebra
- mathematicsalgebra, arithmetic, calculus, geometry, addition
- numbersone, two, four, three, 0
- math conceptsangle, numbers, algebra, circle, equations
complex numbersreal numbers
Complete ordered field
reals · integers · natural numbers · whole numbers · rational numbers
number, complex, complexity, complicated, complication, complicate, complexities, complex number