 | George Chrystal - Algebra - 1886 - 574 pages
...coso' + sino sino') + (sino coso' - coso sin#')t } , = -, { cos(0 -ff) + i sin(6> - o')} (5). Hence the quotient of two complex numbers is a complex number...difference of the amplitudes of the two complex numbers. § 16.] There is an instructive way of looking at the results of last paragraph which is worthy of... | |
 | Arthur Latham Baker - Algebra - 1892 - 98 pages
...ism (<p—<p')] found by multiplying numerator .and denominator by cos <p'—i sin <p'. Consequently, the quotient of two complex numbers is a complex number...difference of the amplitudes of the two complex numbers, If in the above equation, we make r=i, <p=o, we get ii i = — [cos <p' — / sin <p'] a useful transformation... | |
 | George Chrystal - Algebra - 1893 - 604 pages
...sin в sin 0') + (sin в cos 0' - cos в sin 0')t}, = r- {cos ((9 - ff) + i sin (0 - 0')} (5). Hence the quotient of two complex numbers is a complex number...moduli, and whose amplitude is the difference of the amplitude of the two complex numbers. § 16.] There is an instructive way of looking at the results... | |
 | Samuel Marx Barton - Determinants - 1899 - 224 pages
...«'). Then (a + ib) (a' + *b') = №'{cos(a + «') + i sin (a + «')}, which proves that the product of two complex numbers is a complex number, whose modulus is the product of the two moduli, and whose argument is the sum of the two arguments. Similarly, we may prove... | |
 | William Snow Burnside, Arthur William Panton - Determinants - 1899 - 308 pages
...theorem, (a + ib) (a' + ib') = /u/u' (cos (a + a') + » sin (a + a') } , which proves that the product of two complex] numbers is a complex number, whose modulus is the product of the two moduli, and whose amplitude is the sum of the two amplitudes. In the same way it... | |
 | George Chrystal - Algebra - 1904 - 608 pages
...cos 0 sin 0');'}, = f-, {cos (0-ff) + i siii (0-0')} (5). Hence the quotient of two complex nmnlmrs is a complex number whose modulus is the quotient of the moduli, and whose amplitude is to a multiple of 1-a the difference of the amplitude of the two complex IRRATIONAL OPERATIONS WITH... | |
 | George Chrystal - Algebra - 1904 - 606 pages
...6V) r'(cos " - {(cos 0 cos ff + sin 6 sin + (sin 0 cos 0* - cos 0 sin 0')i}, -0')} (5). Hence tlie quotient of two complex numbers is a complex number whose modulus is Uie .quotient of the moduli, and whose amplitude is to a 'multiple of lir the difference of the amplitude... | |
 | George Albert Wentworth - Algebra - 1906 - 440 pages
...ad) V- 1, an orthotomic number ; if be + ad = 0, the product becomes ac - bd, a scalar number. 320. Quotient of Two Complex Numbers. The quotient of two complex numbers is in general a complex number. Divide a + b V- 1 by с + d V- 1. _ (a + b _ (ас + bd) + (be - ad) V^T... | |
 | Joseph Victor Collins - Algebra - 1913 - 362 pages
...+ 2 1 ' 7 + 5t 4 ' 312. Graphical Representation of Division of Complex Numbers. Since the product of two complex numbers is a complex number whose modulus is the product of the given moduli and whose amplitude equals the sum of the given amplitudes, it may be inferred... | |
 | Emil G. Milewski - Mathematics - 1998 - 932 pages
...• PROBLEM 3-7 Using the representation of complex numbers 19 z = re (1) prove that 1. the product of two complex numbers is a complex number whose modulus is the product of the two moduli and whose argument is the sum of the two arguments. 2. the quotient of two... | |
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Hence the quotient of two complex numbers is a complex number whose modulus is the quotient of the moduli, and whose amplitude is the difference of the amplitudes of the two complex numbers. 
