Complex Numbers and Quadratic Equations Formulas for Class 11 Maths Chapter 5
Are you looking for Complex Numbers and Quadratic Equations formulas for class 11 Chapter 5? Today, we are going to share Complex Numbers and Quadratic Equations formulas for class 11 Chapter 5 according to student requirements. You are not a single student who is searching Complex Numbers and Quadratic Equations formulas for class 11 Chapter 5. According to me, thousands of students are searching Complex Numbers and Quadratic Equations formulas for class 11 Chapter 5 per month. If you have any doubt or issue related to Complex Numbers and Quadratic Equations formulas then you can easily connect with through social media for discussion. Complex Numbers and Quadratic Equations formulas will very helpful to understand the concept and questions of the chapter Complex Numbers and Quadratic Equations. I would like to suggest you remember Complex Numbers and Quadratic Equations formulas for the whole life. It also helps you with higher studies.
- Complex number = \( z=a+bi \)
- Conjugate = \( \bar z =a−bi \)
- Symmetry = \( −z=−a−bi \)
- Equality = a+bi=c+di⇔a=c and b=d
- Addition = \( (a+bi)+(c+di)=(a+c)+(b+d)i \)
- Subtraction = \( (a+bi)−(c+di)=(a−c)+(b−d)i \)
- Multiplication = \( (a+bi)\times(c+di)=(ac−bd)+(ad+bc)i \)
- Division = \( \frac{(a+bi)}{(c+di)} = \frac{a+bi}{c+di} \times \frac{c-di}{c-di} = \frac{ac+bd}{c^{2}+d^{2}} + \frac{bc-ad}{c^{2}+d^{2}}\times i \)
- Multiplication Conjugates = \( (a+bi)(a+bi)=a^{2}+b^{2} \)
Powers of Complex Numbers
- i^{n }= i, if n = 4a+1, i.e. one more than the multiple of 4.
Example – i^{1}=i; i^{5}=i; i^{9}=i; i^{4a+1};
- i^{n }= -1, if n = 4a+2, i.e. two more than the multiple of 4.
Example – i^{2}= -1; i^{6}= -1; i^{10}= -1; i^{4a+2};
- i^{n }= -i, if n = 4a+3, i.e. Three more than the multiple of 4.
Example – i^{3}= -i; i^{7}= -i; i^{11}= -i; i^{4a+3};
- i^{n }= -1, if n = 4a, i.e. the multiple of 4.
Example – i^{4}= 1; i^{8}= 1; i^{12}= 1; i^{4a};
\(x^2+bx+c=0 \;where\; a ≠ 0\) |
\(x=-b\pm\frac{\sqrt{b^2-4ac}}{2a}\) |
Summary Complex Numbers and Quadratic Equations Formulas
We have listed top important formulas for Complex Numbers and Quadratic Equations for class 11 Chapter 5 which helps support to solve questions related to chapter Complex Numbers and Quadratic Equations. I would like to say that after remembering the Complex Numbers and Quadratic Equations formulas you can start the questions and answers the solution of the Complex Numbers and Quadratic Equations chapter. If you faced any problem to find a solution of Complex Numbers and Quadratic Equations questions, please let me know through commenting or mail.
NCERT Class 11 Maths Formulas By chapters
- Chapter 1 Sets
- Chapter 2 Relations and Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 7 Permutations and Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences and Series
- Chapter 10 Straight lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction to Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 15 Statistics
- Chapter 16 Probability
NCERT Solutions Class 11 Maths by Chapters
- Chapter 1 Sets
- Chapter 2 Relations and Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations and Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences and Series
- Chapter 10 Straight lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction to Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability