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Multiplication of Complex Numbers - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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Properties of multiplication of Complex Numbers
  1. Closure law: multiplication of two complex numbers is a complex number, i.e. the product z1z2 is a complex number for all complex numbers z1 and z2.
  2. Commutative law: for any two complex numbers  z1 and z2, z1・z2 = z2・z1
  3. Associative law: for any three complex numbers  z1, zand z3 ,  (z1・z2)・z3 =   z1・(z2 ・z3)
  4. Multiplicative identity: if the multiplication of a complex number z1 with another complex number z2 is z1,  then z2 is called the multiplicative identity. We have z・1 = z = 1・z, so 1 is the multiplicative identity.
  5. Multiplicative inverse: For every non-zero complex z = a + ib, (a ≠ 0,b ≠ 0 ) we have the complex number \\\mathrm{\frac{a}{a^2+b^2}+i\frac{-b}{a^2+b^2}\;\;(denoted\;by\;\;\frac{1}{z}\;or\;z^{-1})}  called the multiplicative inverse of z. 
  6. Distributive law : for any three complex numbers  z1, z2 and z3 ,  z1・(z2 + z3) = z1・z2 + z1・z3  and  (z1 + z2)・z3 = z1・z3 + z2・z3

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Properties of multiplication of Complex Numbers

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