Concept of Complex Numbers

Topics

• Sequences and Series
• Concept of Sequences
• Geometric Progression (G.P.)
• General Term Or the nth Term of a G.P.
• Sum of the First n Terms of a G.P.
• Sum of Infinite Terms of a G. P.
• Recurring Decimals
• Harmonic Progression (H. P.)
• Types of Means
• Special Series (Sigma Notation)
• Locus and Straight Line
• Locus
• Equation of Locus
• Line
• Equations of Lines in Different Forms
• General Form Of Equation Of Line
• Determinants
• Determinants
• Properties of Determinants
• Application of Determinants
• Cramer’s Rule
• Consistency of Three Linear Equations in Two Variables
• Area of a Triangle Using Determinants
• Collinearity of Three Points
• Limits
• Definition of Limit of a Function
• Algebra of Limits
• Evaluation of Limits
• Direct Method
• Factorization Method
• Rationalization Method
• Limits of Exponential and Logarithmic Functions
• Continuity
• Continuous and Discontinuous Functions
• Continuity of a Function at a Point
• Definition of Continuity
• Continuity from the Right and from the Left
• Properties of Continuous Functions
• Continuity in the Domain of the Function
• Examples of Continuous Functions Whereever They Are Defined
• Differentiation
• The Meaning of Rate of Change
• Definition of Derivative and Differentiability
• Derivative by the Method of First Principle
• Rules of Differentiation (Without Proof)
• Applications of Derivatives
• Partition Values
• Concept of Median
• Partition Values
• Quartiles
• Deciles
• Percentiles
• Relations Among Quartiles, Deciles and Percentiles
• Graphical Location of Partition Values
• Measures of Dispersion
• Measures of Dispersion
• Range of Data
• Quartile Deviation (Semi - Inter Quartile Range)
• Variance and Standard Deviation
• Standard Deviation for Combined Data
• Coefficient of Variation
• Skewness
• Skewness
• Asymmetric Distribution (Positive Skewness)
• Asymmetric (Negative Skewness)
• Measures of Skewness
• Karl Pearson’S Coefficient of Skewness (Pearsonian Coefficient of Skewness)
• Features of Pearsonian Coefficient
• Bowley’s Coefficient of Skewness
• Bivariate Frequency Distribution and Chi Square Statistic
• Bivariate Frequency Distribution
• Classification and Tabulation of Bivariate Data
• Marginal Frequency Distributions
• Conditional Frequency Distributions
• Categorical Variables
• Contingency Table
• Chi-Square Statistic ( χ2 )
• Correlation
• Correlation
• Concept of Covariance
• Properties of Covariance
• Concept of Correlation Coefficient
• Scatter Diagram
• Interpretation of Value of Correlation Coefficient
• Permutations and Combinations
• Introduction of Permutations and Combinations
• Fundamental Principles of Counting
• Concept of Multiplication Principle
• Concept of Factorial Function
• Permutations
• Permutations When All Objects Are Distinct
• Permutations When Repetitions Are Allowed
• Permutations When All Objects Are Not Distinct
• Circular Permutations
• Properties of Permutations
• Combination
• Properties of Combinations
• Commercial Mathematics
• Percentage
• Profit and Loss
• Simple and Compound Interest (Entrance Exam)
• Depreciation
• Partnership
• Goods and Service Tax (GST)
• Shares and Dividends
• Imaginary number
• Complex Number

Notes

Complex Number is a combination of a real and an imaginary number in the form a + bi. a and b are real numbers, and. i is the "unit imaginary number" sqrt(−1).
For the complex number z = a + ib, a is called the real part, denoted by Re z and b is called the imaginary part denoted by Im z of the complex number z. For example, if z = 2 + i5, then Re z = 2 and Im z = 5.
Two complex numbers z1 = a + ib and z2 = c + id are equal if  a = c and b = d.

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Complex numbers [00:18:28]
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