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" In practice, the quotient of two complex numbers is usually found by multiplying both numerator and denominator by the conjugate of the denominator: o + ib _ a + ib c — id _ ac + bd be — ad . , . , n ^Md " F+ld  "
Practical Algebra (revised) Prepared for the Use of the Midshipmen at the ... - Page 4
by Stimson Joseph Brown, Paul Capron - 1910 - 191 pages
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Text-book of Algebra: With Exercises for Secondary Schools and ..., Part 1

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...
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Higher Algebra

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...
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Elements of Algebra with Exercises

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...
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College Algebra

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...
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Analytic Geometry and Principles of Algebra

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...
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Elementary Mathematical Analysis

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...
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Transmission Line Formulas: A Collection of Methods of Calculation for the ...

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...
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College Algebra

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...
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Mechanism Analysis: Simplified and Graphical Techniques, Second Edition,

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...
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Geometry

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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