| George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1898 - 712 pages
...article that a fraction whose denominator is a complex number can be expressed as a complex number by multiplying both numerator and denominator by the conjugate of the denominator. Ex. 1. 2V-3 " (2V-3)(-2v-3) 12 _ 2 (1 + V- 2)(- 2 y- 3) = - 2 y- 3 + 2 ye " Notice that it was necessary... | |
| George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1901 - 646 pages
...article that a fraction whose denominator is a complex number can be expressed as a complex number by multiplying both numerator and denominator by the conjugate of the denominator. Ex l l+V-2 = (l+V-2)(-V-3) -V-3+ув 2V -3 " (2V-3)(-V-3) " 6 -tve-iV-3. Notice that it was necessary... | |
| George Egbert Fisher, Isaac Joachim Schwatt - 1902 - 504 pages
...article that a fraction whose denominator is a complex number can be expressed as a complex number by multiplying both numerator and denominator by the conjugate of the denominator. Ex l 1+У-2 = (1+У-2)(-У-3)^-у-3+уб 2V -3 (2y-3)(-y-3) 6 Notice that it was necessary to multiply... | |
| Charles Hamilton Ashton, Walter Randall Marsh - Algebra - 1907 - 304 pages
...+ hi) (a — ii) = а2 + b2. A fraction in the form - ^. can be reduced to the c + ai typical form by multiplying both numerator and denominator by the conjugate of the denominator. 2-3 г 2-3 г = (2-Зг)(5-2г) ^ 4-19 t = _4 _ 1ib 5 + 2г (5 + 2 г)(5-2 г) * 25 + 4 29 29г' EXERCISE... | |
| Alexander Ziwet, Louis Allen Hopkins - Geometry, Analytic - 1913 - 396 pages
...numbers. 122. Division. To form the quotient of two complex numbers we may render the denominator reaI, by multiplying both numerator and denominator by the conjugate of the denominator. Thus : *i _ "a + yli _(%i + i \ Here also the result is a complex number. A geometric construction is indicated... | |
| John Wesley Young, Frank Millett Morgan - Functions - 1917 - 586 pages
...complex numbers xl + iy1 and x2 + iy2 may be reduced to the form a + ib if we make the denominator real by multiplying both numerator and denominator by the conjugate of the denominator. Thus, a;2 If we write the two complex numbers in polar form and then perform the division, we have pi (cos... | |
| Herbert Bristol Dwight - Electric lines - 1925 - 238 pages
...performed. A fraction with a complex denominator can be changed directly into a plain complex quantity by multiplying both numerator and denominator by the conjugate of the denominator, that is, a quantity which is the same except that j is replaced by —j. This process is called "rationalizing... | |
| William Le Roy Hart - Algebra - 1926 - 412 pages
...their product are real numbers. A quotient of two complex numbers can be reduced to the form а + Ы by multiplying both numerator and denominator by the conjugate of the denominator. * For a complete logical foundation of the algebra of comp1ex numbers, see Dickson's ELEMENTARY THEORY... | |
| Lyndon O. Barton - Technology & Engineering - 1993 - 744 pages
...ad) " c2 + d2 " c2 + d2 c2 + d2 Note that in the division case, the quotient is conveniently found by multiplying both numerator and denominator by the conjugate of the denominator. 13.3 GEOMETRIC REPRESENTATION OF A COMPLEX VECTOR A complex number is represented geometrically by... | |
| David A. Brannan, Matthew F. Esplen, Jeremy J. Gray - Mathematics - 1999 - 516 pages
...+ 4i, 3,4 + 3i do all lie on a generalized circle. D You met this method of simplifying a quotient by multiplying both numerator and denominator by the conjugate of the denominator earlier, in Subsection 5.2. 1 . In this example we showed that the points /, 1 + 4i, 3,4 + 3i all lie... | |
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