Properties of complex numbers| Proof| properties of complex conjugate|bsc| adp cs скачать в хорошем качестве

Properties of complex numbers| Proof| properties of complex conjugate|bsc| adp cs

This video properties of complex numbers|proof|properties of complex conjugate is an important topic of bsc mathematics ADP CS engineering mathematics class 11 complex numbers class 12 complex numbers. In this video we will learn properties of complex numbers with proof.We will learn conjugate of a complex number. We will operations on complex numbers. We will learn how to add subtract multiply and divide complex numbers. In this video we will learn what is complex numbers. What is number system. What is definition of complex numbers and basics concepts of complex numbers explained with examples. Complex numbers is an important topic of class 11 and complex numbers in class 12 also complex numbers engineering mathematics and complex numbers adp cs 1st semester and complex numbers bsc mathematics. Complex numbers is explained from method by SM Yousuf. In this video we will learn real and imaginary part of complex numbers and how to separate real and imaginary part of complex numbers. We will learn what is imaginary numbers. In the upcoming videos of complex numbers we will learn what is properties of complex numbers operations on complex numbers and what is polar form of complex numbers with examples. We will learn adding subtracting multiplying and dividing complex numbers. We will learn how to convert complex numbers to Polar form. Operations on Complex Numbers: (1) Addition of Complex Number- If z1 = a + ib and z2 = c + id with the two complex number, then their addition is denoted by z1 + z2 and is given as- z1 + z2 = (a + c) + i(b + d) ⇒ z1 + z2 = [Re (z1) + Re (z2)] + i[Im (z1) + Im (z2)] Properties of Addition of Complex Number: Commutative Property- If z1 and z2 be the two complex numbers then z1 + z2 = z2 + z1. Associative Property- If z1, z2, z3 be the three complex numbers then (z1 + z2) + z3 = z1 + (z2 + z3). Additive Identity-If z be any complex number then z + 0 = z = 0 + z, then O is called the additive identity and O = 0 + i0. Additive Inverse- If z1 and z2 be any two complex numbers such that z1 + z2 = 0 = z2 + z1 then z2 is the additive inverse of z1 and in general z2 = -z1. (2) Subtraction of Complex Number- If z1 = a + ib and z2 = c + id be two complex numbers, then the subtraction of z2 from z1 is- z1 – z2 = z1 + (-z2) = (a + ib) + (-c – id) = (a – c) + i(b – d) (3) Multiplication of Complex Number- If z1 = a + ib and z2 = c + id be the two complex numbers then their multiplication is denoted by z1.z2 and is given as- z1 . z2 = (a + ib) (c + id) ⇒ z1 . z2 = ac + i(ad + bc) – bd ⇒ z1 . z2 = (ac – bd) + i(ad + bc) ⇒ z1 . z2 = [Re (z1) . Re (z2) – Im (z1) . Im (z2)] + i[Re (z1) . Im (z2) + Im (z1) . Re (z2)] Properties of Multiplication of Complex Number: Commutative Property- If z1 and z2 be two complex numbers then z1 . z2 = z2 . z1. Associative Property- If z1, z2, z3 be three complex numbers then (z1 . z2) . z3 = z1 (z2 . z3). Multiplicative Identity- If z be any complex number such that z . 1 = z = 1 . z then ‘1’ is called the Multiplicative Identity. Multiplicative Inverse- If z be any complex number such that z . z1 = 1 = z1 . z then z1 is called the multiplicative inverse of z. In general z = 1/z. Example- Find the Multiplicative Inverse of a + ib. Solution: Let z = a + ib then multiplicative inverse of z is 1/(a + ib) ⇒ z = 1/(a + ib) x (a – ib)/(a – ib) ⇒ z = (a – ib)/[a2 – (ib)2] ⇒ z = (a – ib)/(a2 + b2) ⇒ z = z̄/| z |2 (4) Division of Complex Number- If z1 = a + ib and z2 = c + id are two complex numbers, then the division of z1 by z2 is defined as- z1/z2 = (a + ib)/(c + id) ⇒ z1/z2 = (a + ib).(c – id)/(c + id).(c – id) ⇒ z1/z2 = [(ac + bd) + i(bc – ad)]/(c2 + d2) ⇒ z1/z2 = (ac + bd)/(c2 + d2) + i (bc – ad)/(c2 + d2) Conjugate of a Complex Number: If z be any complex number such that z = a + ib then its conjugate is denoted by z̄ and is given as z̄ = a – ib. Properties of Conjugate of a Complex Number: If z, z1, z2 be any complex number then- Complex numbers|basic concepts|properties|polar form|de moivre's theorem|important questions playlist 👇🏻    • Complex numbers|basic concepts|properties|...   Learn N upswing 🌼 Don't forget to subscribe thank you ☺️ #propertiesofcomplexnumbers, #propertiesofcomplexconjugate, #complexnumbers, #definitionofcomplexnumbersmethodbysmyousuf, #conjugateofcomplexnumber, #operationoncomplexnumbers, #complexnumbersengineeringmathematics, #complexnumbersclass11, #addingcomplexnumbers, #substractingcomplexnumbers, #multiplyingcomplexnumbers, #dividingcomplexnumbers, #complexnumbersclass12, #complexnumbersadpcs, #complexnumbersexplainedwithexamples, #complexnumbersrealandimaginarypart, #learnnupsiwng,