 | Royal Irish Academy - Science - 1847 - 678 pages
...or — : — -, the modulus of the triplet, it cos* sin* will be true to say that the modulus of the product is equal to the product of the moduli of the factors. The third equation asserts, that the amplitude of the product is equal to the sum of the amplitudes of... | |
 | Henry Burchard Fine - Algebra - 1890 - 154 pages
...interpretation to give ij. It would not do to set it equal to a'-f- ib'+jc', for then the theorem that the modulus of a product is equal to the product of the moduli of its factors, which it seemed indispensable to maintain, would lose its validity ; unless, indeed, a'... | |
 | Ernest William Hobson - Exponential functions - 1891 - 380 pages
...#2), their product may be written r,r2 (cos (#, + #2) + i sin (0, + $2)} ; this expression shews that the modulus of a product is equal to the product of the moduli, and the argument of the product is equal to the sum of the arguments of the two quantities. We can... | |
 | Sir James Hopwood Jeans, James Jeans - Kinetic theory of gases - 1904 - 378 pages
...write the equation in the form X + iY^ — fa-fae-t* .......................... (490), ap and, since the modulus of a product is equal to the product of the moduli of its factors, it follows at once that *'+r'-~|fi|v-«* ........................... (49i). Since, from... | |
 | William Henry Metzler, Edward Drake Roe, Warren Gardner Bullard - Algebra - 1908 - 372 pages
...extended to three factors. And in a similar way we obtain for any number of factors : The modulus of the product is equal to the product of the moduli of the factors. The argument of the product is equal to the sum of the arguments of the factors. Applying these principles to the present... | |
 | William Henry Metzler, Edward Drake Roe, Warren Gardner Bullard - Algebra - 1908 - 370 pages
...at once from 131, where it is shown that in the product of two complex numbers, the modulus of the product is equal to the product of the moduli of the factors, and the argument of the product is equal to the sum of the arguments of the factors, two factors being... | |
 | Leonard Eugene Dickson - Mathematics - 1923 - 358 pages
...area comprised between the vector 00, the a;-axis, and |z — Z)ij2=l. The modulus of a product is the product of the moduli of the factors. The argument of a product is the sum of the arguments (properly chosen) of the factors. Part III (pp. 209-226) treats of the representation of forms by lattices.... | |
 | James Jeans - Electric power - 1951 - 676 pages
...this result to any number of factors. Thus we have the important rules : The modulus of a product is the product of the moduli of the factors. The argument of a product is tfte sum of the arguments of tlie factors. There is a geometrical interpretation of multiplication.... | |
 | English periodicals - 1846 - 604 pages
...write, generally, TIIQ = nTQ; UnQ = HUQ. It was indeed shown, so early as in the 3rd article, that the modulus of a product is equal to the product of the moduli ; but the process by which an equivalent result has been here deduced does not essentially depend upon... | |
 | John Stillwell - Mathematics - 2004 - 576 pages
...for his fundamental formula was the multiplicative property of the absolute value, or as he put it: "the modulus of a product is equal to the product of the moduli of the factors." This generalizes the multiplicative property of the absolute value for complex numbers, and shows that... | |
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... the modulus of a product is equal to the product of the moduli of the factors. 