Addition of complex number and properties simple method JEE
In this video explained Addition of complex number and properties simple method JEE. This topic is in class 11. The addition of complex numbers is the process of combining two or more complex numbers to form a new complex number. The sum of two complex numbers z1 = a1 + b1i and z2 = a2 + b2i is given by
z1 + z2 = (a1 + a2) + (b1 + b2)i
where a1 and a2 are the real parts of the complex numbers and b1 and b2 are the imaginary parts of the complex numbers. The addition of complex numbers is associative commutative and distributive over scalar multiplication.
Here are some important properties of the addition of complex numbers
Commutativity For any two complex numbers z1 and z2, z1 + z2 = z2 + z1.
Associativity For any three complex numbers z1 z2 and z3 (z1 + z2) + z3 = z1 + (z2 + z3).
Distributivity over scalar multiplication For any complex number z and any scalar c c * z + c * z = (c + c) * z.
Existence of additive identity There exists a complex number 0 + 0i called the additive identity such that for any complex number z z + 0 + 0i = 0 + 0i + z = z.
Existence of additive inverse For any complex number z there exists a complex number -z called the additive inverse such that z + (-z) = (-z) + z = 0 + 0i.
These properties of the addition of complex numbers are used in a variety of mathematical and scientific applications including the study of complex analysis linear algebra and electrical engineering. The addition of complex numbers is also a useful tool for understanding the properties of complex numbers and for solving problems involving complex numbers.
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