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.
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.
1. The document discusses methods for calculating the area of regions bounded by curves using integral calculus.
2. Six methods are presented for computing the area of regions bounded above and below by curves including the use of polar coordinates.
3. One example calculates the area between the curves y=x2 and y=2x from x=0 to x=2 as 8π/15 using the integral of the difference of the two curves.
1. The document discusses methods for calculating the area of regions bounded by curves using integral calculus.
2. Six methods are presented for computing the area of regions bounded above and below by curves including the use of polar coordinates.
3. One example calculates the area between the curves y=x2 and y=2x from x=0 to x=2 as 8π/15 using the integral of the difference of the two curves.