Complex Numbers
| Example | Meaning and verbal equivalent | Remarks |
|---|---|---|
| i j | imaginary unit; i² = −1 | In electrotechnology, j is generally used. |
| Re z | real part of z | z = x + iy, where x = Re z and y = Im z |
| Im z | imaginary part of z | |
| ∣z∣ | absolute value of z; modulus of z | mod z is also used |
| arg z | argument of z; phase of z | z = reiφ, where r = ∣z∣ and φ = arg z, i.e. Re z = r cos φ and Im z = r sin φ |
| z* | (complex) conjugate of z | sometimes a bar above z is used instead of z* |
| sgn z | signum z | sgn z = z / ∣z∣ = exp(i arg z) for z ≠ 0, sgn 0 = 0 |
Read more about this topic: ISO 31-11
Famous quotes containing the words complex and/or numbers:
“In the case of all other sciences, arts, skills, and crafts, everyone is convinced that a complex and laborious programme of learning and practice is necessary for competence. Yet when it comes to philosophy, there seems to be a currently prevailing prejudice to the effect that, although not everyone who has eyes and fingers, and is given leather and last, is at once in a position to make shoes, everyone nevertheless immediately understands how to philosophize.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“Think of the earth as a living organism that is being attacked by billions of bacteria whose numbers double every forty years. Either the host dies, or the virus dies, or both die.”
—Gore Vidal (b. 1925)