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Multiplication of Complex Numbers - Practice Questions & MCQ
Updated on Sep 18, 2023 18:34 AM | #JEE Main
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Properties of multiplication of Complex Numbers
- 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.
- Commutative law: for any two complex numbers z1 and z2, z1・z2 = z2・z1
- Associative law: for any three complex numbers z1, z2 and z3 , (z1・z2)・z3 = z1・(z2 ・z3)
- 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.
- Multiplicative inverse: For every non-zero complex z = a + ib, (a ≠ 0,b ≠ 0 ) we have the complex number $\frac{a}{a^2+b^2}+i \frac{-b}{a^2+b^2}\left(\right.$ denoted by $\frac{1}{z}$ or $\left.z^{-1}\right)$ called the multiplicative inverse of z.
- 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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