complex plane
Where imaginaries live
The complex plane is a way of representing complex numbers geometrically, with the horizontal axis showing real parts and the vertical axis showing imaginary parts.
Each complex number corresponds to a unique point.
The complex plane makes operations like addition and multiplication visual—adding shifts points, multiplying rotates and scales them.
Absolute value operation
- argumentReasoned case or dispute
- quadrantFourth of a circle
- originStarting point or source
- unit circleRadius-one circle at origin
rotation · reflection · translation · magnitude · Cartesian coordinates · distance · angle · dilation
Modify verbs grammatically
- quadratic formulaEquation solving ax²+bx+c=0
- factorizationDecomposing into multiplicative parts
- eigenvalueScalar satisfying determinant equation
- transcendentalBeyond ordinary experience
Point where values explode
- residueMatter left behind
- poleCylindrical shaft or extremity
- harmonic functionLaplacian equals zero everywhere
Thorough change in form
- bilinearLinear in both arguments
- fixed pointValue unchanged by function
- conformalMaintains angles locally
- isogonalHaving equal angles
domain · range · image · one-to-one · onto · composition
modulus
Absolute value operation
unit circle · rotation · reflection · translation · magnitude · Cartesian coordinates · distance · angle · dilation · inversion
conjugate
Modify verbs grammatically
- quadratic formulaEquation solving ax²+bx+c=0
- factorizationDecomposing into multiplicative parts
- eigenvalueScalar satisfying determinant equation
singularity
Point where values explode
- residueMatter left behind
- poleCylindrical shaft or extremity
- harmonic functionLaplacian equals zero everywhere
transformation
Thorough change in form
- bilinearLinear in both arguments
- fixed pointValue unchanged by function
- conformalMaintains angles locally
isogonal · domain · range · image · one-to-one · onto · composition
complex planenumber line
Diagram showing ordered quantities
real number line · integers · natural numbers · rational numbers
plane, complex, complexity, planes, complicated, complexities, simplex, complexly, complexing