Комплекс тоо цуврал хичээл-1Март The document provides examples of performing arithmetic operations on complex numbers. It shows adding, subtracting, and multiplying complex numbers in the form of a + bi. Examples include combining terms with the same real and imaginary parts and distributing operations across terms. It also demonstrates dividing one complex number by another. The document concludes by stating example 18 builds upon the previous example 17.
Комплекс тоо цуврал хичээл-2Март This document discusses complex numbers and their properties in Mongolian. It defines the modulus of a complex number a + bi as √(a2 + b2). It provides examples of calculating the modulus of 3 + 2i and 4 - 5i. It then discusses the conjugate of a complex number a - bi. Other topics covered include complex number addition, multiplication, division, powers, and properties of polynomials with complex number coefficients. Worked examples are provided to illustrate these concepts and theorems.
Математик индукц Март The document contains three mathematical proofs:
1. Using induction, it is proven that for any natural number n, the sum 2 + 4 + 6 + ... + 2n is equal to n(n+1).
2. Also by induction, it is shown that the sum 1/(3*5) + 1/(5*7) + ... + 1/(2n+1)(2n+3) equals n/(3(2n+3)) for any natural n.
3. Finally, induction is used to prove that for any natural number n, the expression 8n + 6 is divisible by 7.
Комплекс тоо цуврал хичээл-1Март The document provides examples of performing arithmetic operations on complex numbers. It shows adding, subtracting, and multiplying complex numbers in the form of a + bi. Examples include combining terms with the same real and imaginary parts and distributing operations across terms. It also demonstrates dividing one complex number by another. The document concludes by stating example 18 builds upon the previous example 17.
Комплекс тоо цуврал хичээл-2Март This document discusses complex numbers and their properties in Mongolian. It defines the modulus of a complex number a + bi as √(a2 + b2). It provides examples of calculating the modulus of 3 + 2i and 4 - 5i. It then discusses the conjugate of a complex number a - bi. Other topics covered include complex number addition, multiplication, division, powers, and properties of polynomials with complex number coefficients. Worked examples are provided to illustrate these concepts and theorems.
Математик индукц Март The document contains three mathematical proofs:
1. Using induction, it is proven that for any natural number n, the sum 2 + 4 + 6 + ... + 2n is equal to n(n+1).
2. Also by induction, it is shown that the sum 1/(3*5) + 1/(5*7) + ... + 1/(2n+1)(2n+3) equals n/(3(2n+3)) for any natural n.
3. Finally, induction is used to prove that for any natural number n, the expression 8n + 6 is divisible by 7.
LogHuslen ZayaThis document outlines 4 properties of logarithms: 1) the logarithm of a product is equal to the sum of the logarithms of the factors, 2) the logarithm of a quotient is equal to the difference of the logarithms of the dividend and divisor, 3) the logarithm of a power can be written as the exponent multiplied by the logarithm of the base, 4) changing the base of a logarithm results in the new logarithm being equal to the original logarithm divided by the logarithm of the new base.