Abstract
This chapter discusses complex numbers and quaternions. Complex numbers are of the form a + bi where a and b are real numbers, and i2 = −1. Quaternions are a generalization of complex numbers to quadruples that satisfy the quaternion formula i2 = j2 = k2 = −1.
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Notes
- 1.
There is a possibility that the German mathematician, Gauss, discovered quaternions earlier.
- 2.
Eamonn De Valera, a former taoiseach and president of Ireland, was formerly a mathematics teacher, and his interests included maths, physics and quaternions. He is alleged to have carved the quaternion formula on the door of his cell while in prison in Lincoln Jail, England during the Irish struggle for independence from Britain.
- 3.
A non-empty set X with a distance function d is a metric space if
(i) d(x, y) ≥ 0 and d(x, y) = 0 ⇔ x = y
(ii) d(z, y) = d(y, x)
(iii) d(x, y) ≤ d(x, z) + d(z, y).
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O’Regan, G. (2020). Complex Numbers and Quaternions. In: Mathematics in Computing. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-34209-8_26
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DOI: https://doi.org/10.1007/978-3-030-34209-8_26
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