VIT - VITEEE 2025
ApplyNational level exam conducted by VIT University, Vellore | Ranked #11 by NIRF for Engg. | NAAC A++ Accredited | Last Date to Apply: 31st March | NO Further Extensions!
Multiplication of Complex Numbers - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
-
1 Questions around this concept.
Concepts Covered - 1
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
Study it with Videos
Properties of multiplication of Complex Numbers"Stay in the loop. Receive exam news, study resources, and expert advice!"
Get Answer to all your questions
JEE Main Articles
Back to top