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- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
- == The set comprising all rational and irrational numbers is referred to as the real numbers, denoted as \( \mathbb{R} \). ====Terminating Decimal==== A decimal nu... and denominator. They often represent irrational numbers. ===Example=== \( \pi \) (pi) is a well-known n... nt of \( A \). ===Example=== In the set of real numbers \( \mathbb{R} \), two important binary operations
- Chapter 01: Complex Numbers @bsc:notes_of_mathematical_method
- ====== Chapter 01: Complex Numbers ====== {{ :bsc:notes_of_mathematical_method:ch01-methods-ads.jpg?nolink&640x800|Chapter 01 Complex Numbers Methods}} Notes of the book Mathematical Method w... C}$. ==== Contents and summary ==== * Complex numbers * Properties of complex numbers * The Argand's diagram * De Moivre's theorem * Roots of the comple
- Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
- umber:** The field of all rational and irrational numbers is called the real numbers, or simply the "reals," and denoted $\mathbb{R}$. * **Terminating decimal:*... are addition and multiplication in a set of real numbers. * **Complex number:** The number of the form ... am:** The figure representing one or more complex numbers on the complex plane is called argand diagram.
- Chapter 01: Number System @fsc:fsc_part_1_solutions
- ahore. ==== Contents & summary ==== * Rational numbers and irrational numbers * Properties of real numbers * Complex numbers * Operation on complex numbers * Complex numbers as ordered pairs of real numb
- FSc Part 1 (KPK Boards) @fsc
- anned (Handwritten) | ===== Chapter 01: Complex Numbers ===== === Objectives === After reading this uni... t the students will be able to: * know complex numbers, its conjugate and absolute value. * understand algebraic properties of complex numbers. * recongnize real and imaginary parts of different types of complex numbers. * know the solution of simultaneous linear equ
- Unit 1: Complex Numbers (Solutions) @fsc-part1-kpk:sol
- ===== Unit 1: Complex Numbers (Solutions) ===== This is a first unit of the book Mathematics 11 published ... or of the form $(a,b)$ where $a$ and $b$ are real numbers and $i=\sqrt{-1}$. * Recognize $a$ as real pa... $z$. * Know condition for equality of complex numbers. * Carry out basic operations on complex numbers. * Define $\bar{z} = a —ib$ as the complex conjug
- Unit 01: Complex Numbers (Solutions) @math-11-kpk:sol
- ===== Unit 01: Complex Numbers (Solutions) ===== This is a first unit of the book Mathematics 11 published... or of the form $(a,b)$ where $a$ and $b$ are real numbers and $i=\sqrt{-1}$. * Recognize $a$ as real pa... $z$. * Know condition for equality of complex numbers. * Carry out basic operations on complex numbers. * Define $\bar{z} = a —ib$ as the complex conjug
- Question 11 Exercise 6.2 @math-11-kpk:sol:unit06
- shawar, Pakistan. =====Question 11===== How many numbers each lying between $10$ and $1000$ can be formed ... 9$ using only once? ====Solution==== We will form numbers greater than $10$ and less than $1000$. So some ... e digits. Thus we split into two parts as:\\ (i) Numbers greater than $10$ but less than $100$ These numbers will consist just two digits ten digit and unit digit
- MTH321: Real Analysis I (Spring 2023) @atiq
- $\left\{ {{r}_{n}} \right\}$ of distinct rational numbers such that $\underset{n\to \infty }{\mathop{\lim ... s in the 18th century used the entire set of real numbers without having defined them cleanly. The first ri... is no difference between rational and irrational numbers in this regard. </callout> =====Schedule===== ... $\left\{ {{r}_{n}} \right\}$ of distinct rational numbers such that $\underset{n\to \infty }{\mathop{\lim
- Complex Analysis by M Usman Hamid @notes
- e notes. The extension to the concept of complex numbers from that of real numbers was first necessitated by the solution of algebraic equations. For example, the ... for details on topics. * Order pair * Complex numbers * Vectors interpretation on complex numbers (graphical representation) * The modulus or absolute value
- Unit 02: Matrices and Determinants (Solutions) @math-11-kpk:sol
- or of the form $(a,b)$ where $a$ and $b$ are real numbers and $i=\sqrt{-1}$. * Recognize $a$ as real part... f $z$. * Know condition for equality of complex numbers. * Carry out basic operations on complex numbers. * Define $\bar{z} = a —ib$ as the complex conjugate ... +ib$ * Describe algebraic properties of complex numbers (e.g. commutative, and distributive) with respect
- Multiple Choice Questions (BSc/BS/PPSC) by Akhtar Abbas @notes
- for the following subjects are given. - Complex Numbers - Groups - Matrices - System of Linear Equa... inite Series Here are few samples: \\ - Complex numbers with 0 as real part are called: - imaginary numbers - pure non real numbers - pure imaginary numbers - pure complex numbers - For any positive i
- Question 3 & 4 Exercise 4.3 @math-11-kpk:sol:unit04
- kistan. =====Question 3===== Find sum of all the numbers divisible by $5$ from $25$ to $350$. GOOD ====Solution==== The numbers divisible by $5$ from $25$ tò $350$ are\\ $$25,30... end{align} =====Question 4===== The sum of three numbers in an arithmetic sequence is $36$ and the sum of ... d them. ====Solution==== Let us suppose the three numbers are $a-d, a, a+d$\\. then by first condition the
- Question 5 & 6 Exercise 4.3 @math-11-kpk:sol:unit04
- shawar, Pakistan. =====Question 5===== Find four numbers in an arithmetic sequence, whose sum is $20$ and ... squares is $120$ . ====Solution==== Let the four numbers are\\ $$a-2 d, a-d, a+d, a+2 d,$$ $Condition-1$\\... d= \pm 1\end{align} When $a=5$ and $d=1$ then the numbers are\\ \begin{align} a-3d&=5-3=2, \\ a-d&=5-1=4, \... =5+3=8.\end{align} When $a=5$ and $d=-1$ then the numbers are\\ \begin{align}a-3 d&=5-3(-1)=8, \\ a-d&=5-(-
- MTH321: Real Analysis I (Fall 2022) @atiq
- s in the 18th century used the entire set of real numbers without having defined them cleanly. The first ri... is no difference between rational and irrational numbers in this regard. </callout> =====Schedule===== ... ://en.wikipedia.org/wiki/Construction_of_the_real_numbers * http://mathworld.wolfram.com/SquareRoot.html * https://www.mathsisfun.com/numbers/infinity.html * http://en.wikipedia.org/wiki/Re