TAILIEUCHUNG - Mathematics - Lecture 6: The set of complex numbers

Mathematics - Lecture 6 "The set of complex numbers" presents the following content: Properties of complex numbers, conjugate of a complex number, operations involving complex numbers, addition and subtraction of complex numbers, multiplication and division of complex numbers. | The Set of Complex Numbers Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 6 Math 17 (UP-IMath) The Set of Complex Numbers Lec 6 1 / 15 Outline 1 The Set of Complex Numbers Properties of Complex Numbers Conjugate of a Complex Number Operations Involving Complex Numbers Addition and Subtraction of Complex Numbers Multiplication and Division of Complex Numbers The Powers of i Math 17 (UP-IMath) The Set of Complex Numbers Lec 6 2 / 15 The Set of Complex Numbers Recall: There is no real number b such that b2 = −1. Math 17 (UP-IMath) The Set of Complex Numbers Lec 6 3 / 15 The Set of Complex Numbers Recall: There is no real number b such that b2 = −1. We define i to be a number such that i2 = −1. Math 17 (UP-IMath) The Set of Complex Numbers Lec 6 3 / 15 The Set of Complex Numbers Recall: There is no real number b such that b2 = −1. We define i to be a number such that i2 = −1. A complex number is a number of the form a + b · i, where a and b are real numbers. Math 17 (UP-IMath) The Set of Complex Numbers Lec 6 3 / .

• Toán học
• Lecture Mathematics
• Complex numbers
• Set of complex numbers
• Properties of complex numbers
• Conjugate of a complex number
• Operations involving complex numbers
• Lecture Business mathematics
• Bài giảng Toán kinh doanh
• Business mathematics
• Financial mathematics
• Net present value
• Internal rate of return
• Mathematics 53
• Lecture Mathematics 53
• Integrals yielding logarithmic
• Exponential functions
• Integrals of exponential functions
• Natural logarithmic function
• Inverse circular functions
• Integrals yielding
• Derivatives of inverse circular functions
• Graphs of inverse circular functions
• Hyperbolic functions
• Inverse hyperbolic functions
• Derivatives of hyperbolic functions
• Indeterminate forms
• L’Hôpital’s rule
• Polynomial functions
• Basic types of functions
• Constant functions
• Linear functions
• Limit of a function
• One sided limits
• Limit theorems
• One sided limit
• Infinite limits
• The greatest integer function
• Vertical asymptotes
• Infinity formal definition
• Intuitive definition
• Horizontal asymptotes
• Continuity of functions
• Continuity on an interval
• Essential discontinuity
• The intermediate value theorem
• The squeeze theorem
• Trigonometric functions
• Continuity of trigonometric functions
• Differentiation rules
• The tangent line
• Definition of the derivative
• The chain rule
• Chain rule theorem
• Funtion theorem
• Geometric interpretation of differentiability
• Higher order derivatives
• Implicit differentiation
• Local linear approximation
• Rates of change
• Rectilinear motion
• Position function
• Instantaneous velocity
• Related rates
• Function of time
• Problem on related rates
• Numerical facts
• Mean value theorem
• Relative extrema
• Critical numbers
• Decreasing functions
• The second derivative test
• Points of inflection
• Graphing polynomials
• Second derivative
• Graphing functions
• Vertical asymptotes
• Oblique asymptotes
• Absolute extrema
• Bounded intervals
• One relative extremum
• Absolute maximum
• Optimization word problems
• Optimization problems
• Solving optimization problems
• Integration by substitution
• Theorems on antidifferentiation
• Substitution rule
• Particular antiderivatives
• Application to rectilinear motion
• Plane region
• The definite integral
• Properties of the definite integral
• General antiderivative
• The second fundamental theorem of calculus
• Arc length
• Area of a plane region
• Horizontal rectangles