 | James Morford Taylor - 1904 - 192 pàgines
...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... | |
 | John Wesley Young, Frank Millett Morgan - 1917 - 584 pàgines
...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... | |
 | Helen Abbot Merrill - 1917 - 282 pàgines
...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 . • .,... | |
 | Arthur McCracken Harding, George Walker Mullins - 1928 - 344 pàgines
...cos2 02 + sin2 02 = — [cos (0i - 02) + i sin (0i - 02)]. 7*2 Thus we have: The absolute value of the quotient of two complex numbers is equal to the quotient of the absolute values and the angle of the quotient is equal to the angle of the dividend minus the angle... | |
 | G. H. Hardy - 2008 - 21 pàgines
...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... | |
 | Joseph Bak, Donald J. Newman - 1982 - 414 pàgines
...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... | |
 | 2007 - 532 pàgines
...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... | |
 | H.K. Dass & Rama Verma - 1032 pàgines
...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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The modulus of the quotient of two complex numbers is equal to the quotient of their moduli. 