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" The modulus of the quotient of two complex numbers is equal to the quotient of their moduli. "
Plane and Spherical Trigonometry - Page 129
by James Morford Taylor - 1905 - 234 pages
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Plane Trigonometry

James Morford Taylor - History - 1904 - 192 pages
...cos пф + i sin пф = (cos ф + i sin 0)" = cos" 0 + i - cos"-1 0 sin 0 + i2 ^^- - 1 cos"-2 ф sin2 0 Substituting for i2, i3, • • • their values,...i sin ф has q, and only q, unequal qth roots. If n is any integer, then, by § 21, we have cos <f, + г sin ф = cos (2 nir + ф) + г sin (2 итг...
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Elementary Mathematical Analysis

John Wesley Young, Frank Millett Morgan - Functions - 1917 - 584 pages
...02)] p2(cos202 + sin202) = Pi [cos (gi - 02) -f- * sin (0i - 0,)]. P2 Therefore, the absolute value of the quotient of two complex numbers is equal to the quotient of their absolute values, and the angle of the quotient is equal to the difference of their angles. EXAMPLE...
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A First Course in Higher Albegra

Helen Abbot Merrill - Algebra - 1917 - 282 pages
...of the moduli of a + bi and c + di. + (ad + be)2 = Vazcz+~lzd?~+~a?cP + 192. Theorem. The modulus of the quotient of two complex numbers is equal to the quotient of their moduli. Let the two numbers be a +bi and c + di. To prove ,, . ,, ,, f ac + bd . be— ad . • .,...
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A Course of Pure Mathematics Centenary Edition

G. H. Hardy - Mathematics - 2008 - 21 pages
...z. We can now state the theorems for quotients which correspond to (2) and (3). (4) The modulus of the quotient of two complex numbers is equal to the quotient of their moduli. (5) The amplitude of the quotient of two complex numbers is either equal to the difference...
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Complex Analysis

Joseph Bak, Donald J. Newman - Analytic functions - 1982 - 414 pages
...0) where z = rcisO and w = s cis <j> / 0. From the definition of ^, we observe that the modulus of the quotient of two complex numbers is equal to the quotient of their moduli, and arg (^H = arg z— arg w. From 1.2.2 and the definition of a quotient, we obtain the usual...
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G.H. Hardy

2007 - 532 pages
...z. We can now state the theorems for quotients which correspond to (2) and (3). (4) The modulus of the quotient of two complex numbers is equal to the quotient of then* moduli. (5) The amplitude of the quotient of two complex numbers is either equal to the difference...
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S.Chand’S Mathematics For Class XI

H.K. Dass & Rama Verma - Mathematics - 1032 pages
...z2 = ...= za = z, we get (z") = (z)" • z, z, Property 9. I — = =• ie \Z2j Z2 The conjugate of quotient of two complex numbers is equal to the quotient of their conjugates. Proof: Let z, = a + ib and z2 = с + id, then rz, ] ( a+ib\ (a+ib c-id} = = x z2) \c+id)...
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