Negative or Complex Square
If S < 0, then its principal square root is
If S = a+bi where a and b are real and b ≠ 0, then its principal square root is
This can be verified by squaring the root. Here
is the modulus of S. The principal square root of a complex number is defined to be the root with the non-negative real part.
Read more about this topic: Methods Of Computing Square Roots
Famous quotes containing the words negative, complex and/or square:
“The idealist’s programme of political or economic reform may be impracticable, absurd, demonstrably ridiculous; but it can never be successfully opposed merely by pointing out that this is the case. A negative opposition cannot be wholly effectual: there must be a competing idealism; something must be offered that is not only less objectionable but more desirable.”
—Charles Horton Cooley (1864–1929)
“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)
“Interpreting the dance: young women in white dancing in a ring can only be virgins; old women in black dancing in a ring can only be witches; but middle-aged women in colors, square dancing...?”
—Mason Cooley (b. 1927)