 | 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... | |
 | 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... | |
 | 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... | |
 | Charles Sumner Slichter - Functions - 1914 - 520 pages
...10. Find the value of 4V2(cos 75° +i sin 75°) -5- (V3 + i). 221. Quotient of Two Complex Numbers. The quotient of two complex numbers is a complex number...difference of the amplitudes of the two complex numbers. Let the complex numbers be: Zi = x\ + y\i = ri(cos 6! + i sin 0i) zi = X2 + yii = r2 (cos 02 + i sin... | |
 | 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... | |
 | Mario Gonzalez - Mathematics - 1991 - 796 pages
...the same as the integer n(zbz2) given in the statement above. Theorem 1.8 The quotient of two nonzero complex numbers is a complex number whose modulus is the quotient of the modulus of the dividend by the modulus of the divisor and whose argument is the difference between... | |
 | Ushri Datta, A. S. Muktibodh - Algebra - 2006 - 358 pages
...= ri7-2 = Zi | ' | 22 | (9.19) and arg(zi • 22) = 0! + 02 = arg 2! + arg 22 (9.20) Thus, product of two complex numbers is a complex number whose modulus is the product of their moduli and whose amplitude is the sum of their amplitudes. If we use the exponential... | |
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Moivre's 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. 