Number And Its Algebra Syllabus of Lectures On the Theory of Number And Its Al
Number And Its Algebra Syllabus of Lectures On the Theory of Number And Its Al
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We have seen (§ 188) the two-dimensional nature of complex number, and the infinite variety of ways in which it may vary continuously from a -\- hi to c -f di, because the protomonic and neomonic parts may vary independently.
In order that x -\- yl shall become zero, x and y must vanish simultaneously. Por, li x -\- yi = 0, ic = — yi, and hence cc = and y = 0, — else would a protomonic number equal a neomonic, Avhich is impossible except both be zero. (Vide § 183. ) On the other hand, if either... x or y becomes infinite, x -{- yi=cc. (FicZe§198).
120 NUMBER AND ITS ALGEBRA.
194. Li a -\- bi = G -\- di, then a = c and b = d.
For, subtracting c -f- di from each member of the given equation, a — c-\-(b — d)i = 0; therefore, by Section 193, d — c = and b — d ^= ; that is, a = c and b = d.
Of course, since x + (— y) = x — (+ y) ox x — y {% 120), the preceding formula inckides all combinations as a, b, c, and d are positive or negative ; e. G. , if a -f bi = c — di, a = c, b = — d.
What to read after Number And Its Algebra Syllabus of Lectures On the Theory of Number And Its Al?
You can find similar books in the "Read Also" column, or choose other free books by Arthur Lefevre to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
We have seen (§ 188) the two-dimensional nature of complex number, and the infinite variety of ways in which it may vary continuously from a -\- hi to c -f di, because the protomonic and neomonic parts may vary independently.
In order that x -\- yl shall become zero, x and y must vanish simultaneously. Por, li x -\- yi = 0, ic = — yi, and hence cc = and y = 0, — else would a protomonic number equal a neomonic, Avhich is impossible except both be zero. (Vide § 183. ) On the other hand, if either... x or y becomes infinite, x -{- yi=cc. (FicZe§198).
120 NUMBER AND ITS ALGEBRA.
194. Li a -\- bi = G -\- di, then a = c and b = d.
For, subtracting c -f- di from each member of the given equation, a — c-\-(b — d)i = 0; therefore, by Section 193, d — c = and b — d ^= ; that is, a = c and b = d.
Of course, since x + (— y) = x — (+ y) ox x — y {% 120), the preceding formula inckides all combinations as a, b, c, and d are positive or negative ; e. G. , if a -f bi = c — di, a = c, b = — d.
What to read after Number And Its Algebra Syllabus of Lectures On the Theory of Number And Its Al?
You can find similar books in the "Read Also" column, or choose other free books by Arthur Lefevre to read onlineMoreLess
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