Abstract
A complex number z is a number of the form a + bi where a and b are real numbers and i 2 = − 1. Cardona, who was a sixteenth century Italian mathematician, introduced complex numbers, and he used them to solve cubic equations. The set of complex numbers is denoted by ℂ, and each complex number has two parts namely the real part Re(z) = a, and the imaginary part Im(z) = b. The set of complex numbers is a superset of the set of real numbers, and this is clear since every real number is a complex number with an imaginary part of zero. A complex number with a real part of zero (i.e. a = 0) is termed an imaginary number. Complex numbers have many applications in physics, engineering and applied mathematics.
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Notes
- 1.
There is a possibility that the German mathematician, Gauss, discovered quaternions earlier.
- 2.
Eamonn DeValera, 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 when in prison 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) ³ 0 and d(x, y) = 0 Ûx = y
(ii) d(z, y) = d(y, x)
(iii) d(x, y) £ d(x, z) + d(z, y)
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© 2013 Springer-Verlag London
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O’Regan, G. (2013). Complex Numbers and Quaternions. In: Mathematics in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-4534-9_14
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DOI: https://doi.org/10.1007/978-1-4471-4534-9_14
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