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Exercise 2.6 (Solutions) @matric:9th_science:unit_02
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ac{\overline{z}}{\overline{w}}$ * (v) $\frac{1}{2}(z+\overline{z})$ is real part of z * (vi) $\frac{1}{2i}(z-\overline{z})$ is ... &= \frac{1}{2}(4)\\ &= 2 \hbox{ (it is real part of } z). \end{array}$$ 6(vi) $$\begin{array}{cl} \frac{1}{2i}(z-\overline{z}) &= \frac{1}{2}(2+3i-(2-3i))\\ &= \frac{1}{2}(2+3i-2+3i)\\
MCQs: Ch 04 Quadratic Equations @fsc-part1-ptb:mcq-bank
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lgebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The... nd of the page. ====MCQs==== - An equation $ax^2+bx+c=0$ is called - Linear - Quadratic ... - None of these - For a quadratic equation $ax^2+bx+c=0$ - $b \neq 0$ - $c \neq 0$ - $... - None of these - An expression of the form $ax^2+bx+c$ is called - Polynomial - Equation
Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
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ons) ====== <lead>Notes (Solutions) of Exercise 1.2: Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore.... topics of this exercise are complex numbers, real part and imaginary part of complex numbers, properties of the fundamental operation on complex numbers, comp... \right)\nonumber \] </panel> <panel> **Question 2** Verify the multiplication properties of the com
MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
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lgebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The... style{\frac{3}{10}})$ - $\displaystyle{\frac{3}{2+2i}}=$ - $1-i$ - $1+i$ - $-2i$ - ... isplaystyle{\frac{3-3i}{4}}$ - $\overline{z_1+z_2}=$ - $\overline{z_1}+\overline{z_2}$ - $\overline{z_1}-\overline{z_2}$ - $\overline{z_1}
Question 7, Exercise 1.2 @fsc-part1-kpk:sol:unit01
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=&\dfrac{4}{29}+\dfrac{19}{29}i \end{align} Real part $=\dfrac{4}{29}$\\ Imaginary part $=\dfrac{19}{29}$ =====Question 7(ii)===== Separate into real and imaginary parts $\dfrac{{{\left... \ =&\dfrac{-3}{2}-\dfrac{1}{2}i\end{align} Real part $=\dfrac{-3}{2}$ \\ Imaginary part $=-\dfrac{1}{2}$ =====Question 7(iii)===== Separate into real and imaginary parts $\dfrac{1-i}{{{
Question 7, Exercise 1.2 @math-11-kpk:sol:unit01
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=&\dfrac{4}{29}+\dfrac{19}{29}i \end{align} Real part $=\dfrac{4}{29}$\\ Imaginary part $=\dfrac{19}{29}$ =====Question 7(ii)===== Separate into real and imaginary parts $\dfrac{{{\left... \ =&\dfrac{-3}{2}-\dfrac{1}{2}i\end{align} Real part $=\dfrac{-3}{2}$ \\ Imaginary part $=-\dfrac{1}{2}$ =====Question 7(iii)===== Separate into real and imaginary parts $\dfrac{1-i}{{{
Unit 02: Differentiation @fsc:fsc_part_2_solutions
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===== Unit 02: Differentiation ====== {{ :fsc:fsc_part_2_solutions:fsc-2-unit-02-ptb.jpg?nolink|Unit 02: Differentiation}} Notes (Solutions) of Unit 02: ... ion, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You... er the derivative just take a print of [[FSc: FSc Part 2 Important Derivatives & Integrals|Important Deriv... ype="success" icon="fa fa-download"> * Exercise 2.1 | [[vfsc2>ch02:view&cp=01&p=07&ch=02&fp=Ex-2-1-FSC-part2-ver3-1|View Online]] | [[pdf>files/fsc/fsc_part2
Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
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tions) ====== <lead>Notes (Solutions) of Exercise 2.8: Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore.... KISTAN. \\ Page URL: https://www.mathcity.org/fsc-part1-ptb/sol/unit-02/ex2-8 \\ **License:** These resources are shared
Chapter 02: Sets, Functions and Groups @fsc:fsc_part_1_solutions
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-I), Punjab Text Book Board, Lahore. {{ :fsc:fsc_part_1_solutions:fsc-1-chap-02-ptb.jpg?nolink|Chapter 02: Sets, Functions and Groups}} ==== Contents & su... s * Exercise 2.8 ====Erratum=== * Exercise 2.2, Question 4, Part iii, the answer is wrong. The correct answer is: ... ype="success" icon="fa fa-download"> * Exercise 2.1 | [[vfsc1>ch02:view&cp=01&p=06&ch=02&fp=Ex-2-1-FSC-part1-ver1|View Online]] | {{ :fsc:fsc_part_1_solutions:ex-2-1-fsc-part1-ver1.pdf |Download PDF}} * Exercise 2.2 | [[vfs
View Online (Solutions of Unit 02) @fsc:fsc_part_2_solutions:ch02
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all exercises of Unit 02==== * [[mdoku>fsc:fsc_part_2_solutions:ch02:viewer&cp=01&p=06&ch=02&fp=Ex_2_1_FSC_part2|Exercise 2.1]] * [[mdoku>fsc:fsc_part_2_solutions:ch02:viewer&cp=01&p=03&ch=02&fp=Ex-2-2-FSc-part2-ver-2-3|Exercise 2.2]] * [[mdoku>fsc:fsc_part_2_solutions:ch02:viewer&cp=01&p=06&ch=02&fp=Ex_2_3_FSC_part2|Exercise 2.3]] * [[mdoku>fsc:fsc_part_2_solutions:ch02:viewer&cp=01&p=07&ch=02&fp=Ex-2-4-FSc-part2-ver-2-4|Exercise 2.4]] * [[mdoku>fsc:fsc_part_2_solutions:ch02:viewer&cp=01&p=
Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
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esponds to the horizontal axis, and the imaginary part \( y = 2 \) corresponds to the vertical axis. Thus, \( z \... would be plotted as a point at coordinates \( (3, 2) \) on the Argand diagram. ====Modulus of Comple... of its real and imaginary parts: \( |z| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \). Therefore, \( |z| = 5 \). =====Chapter 02: Set and Operat
Chapter 04: Quadratic Equations @fsc:fsc_part_1_solutions
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_4_1_FSC_part1.pdf|Download PDF]] * Exercise 4.2 | [[mdoku>fsc:fsc_part_1_solutions:ch04:viewer&cp=1&p=13&ch=04&fp=Ex_4_2_FSC_part1|View Online]] | [[pdf>files/fsc/fsc_part1/ch04/dn.php?file=Ex_4_2_FSC_part1.pdf|Download PDF]] * Exercise 4.3 | [[mdoku>fsc:fsc_part_1_solutions:c... wnload PDF]] * Exercise 4.7 | [[mdoku>fsc:fsc_part_1_solutions:ch04:viewer&cp=1&p=2&ch=04&fp=Ex_4_7_FSC_part1|View Online]] | [[pdf>f
Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
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has only a finite number of digits in its decimal part, is called terminating decimal.\\ e.g. 0.33333... and 21.134134... is examples of terminating decimal. ... s called complex number. Here $x$ is called real part and $y$ is called imaginary part of $z$.\\ e.g. $2, 3+\sqrt{3}i, \frac{1}{2}+i$. * **Real plane or coordinate plane:** T... ted by $|x+iy|$ or $|(x,y)|$. ===== Chapter 02: Functions and groups ===== * **Set:** A set is... elements within brackets.\\ e.g. $\mathbb{N}=\{1,2,3,4,...\}$ * **Set-builder method:** In this f
Unit 01: Functions and Limits @fsc:fsc_part_2_solutions
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Unit 01: Functions and Limits ====== {{ :fsc:fsc_part_2_solutions:fsc-2-unit-01-ptb.jpg?nolink|Unit 01: Functions and Lim... its, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. The... fa-download"> * Exercise 1.1 | [[mdoku>fsc:fsc_part_2_solutions:ch01:viewer&cp=1&p=11&ch=01&fp=Ex_1_1_F... x_1_1_FSC_part2.pdf|Download PDF]] * Exercise 1.2 | [[mdoku>fsc:fsc_part_2_solutions:ch01:viewer&cp=1&p=5&ch=01&fp=Ex_1_2_
Unit 06: Conic Section @fsc:fsc_part_2_solutions
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====== Unit 06: Conic Section ====== {{ :fsc:fsc_part_2_solutions:fsc-2-unit-06-ptb.jpg?nolink|Unit 06: Conic Section}} N... ion, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You... fa-download"> * Exercise 6.1 | [[mdoku>fsc:fsc_part_2_solutions:ch06:view&cp=01&p=15&ch=06&fp=Ex-6-1-FS... -part2-ver3-1|View Online]] | [[pdf>files/fsc/fsc_part2/ch06/dn.php?file=Ex-6-1-FSC-part2-ver3-1.pdf|Download PDF]] (249kB) * Exercise 6.2 | [[mdoku>fsc:fsc_part_2_s
FSc
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Unit 03: Integration @fsc:fsc_part_2_solutions
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FSc Part 1 (KPK Boards) @fsc
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MCQs by Nauman Idrees @fsc:fsc_part_1_mcqs
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FSc/ICS Part 2 Solutions @fsc
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FSc Part 2 (KPK Boards) @fsc
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MCQs by Muhammad Imran Qureshi @fsc:fsc_part_2_mcqs
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Amir Shehzad @people
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MCQs by Nauman Idrees @fsc:fsc_part_2_mcqs
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MCQs by Muhammad Imran Qureshi @fsc:fsc_part_1_mcqs
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Exercise 2.5 (Solutions) @matric:9th_science:unit_02
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Question 8, Exercise 1.2 @fsc-part1-kpk:sol:unit01
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Question 8, Exercise 1.2 @math-11-kpk:sol:unit01
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Syllabus for UoS (Private only) @msc:syllabus
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FSc/ICS Part 2 (Mathematics): PTB
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FSc Part 2 Model Papers @fsc
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Chapter 01: Number System @fsc:fsc_part_1_solutions
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Unit 07: Vectors @fsc:fsc_part_2_solutions
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Unit 1: Complex Numbers (Solutions) @fsc-part1-kpk:sol
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Unit 01: Complex Numbers (Solutions) @math-11-kpk:sol
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MCQs/Objective: HSSC-II @fsc
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Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
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CHEM-501: Basic Mathematics for Chemist @atiq
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MCQs with Answers @fsc:fsc_part_1_mcqs
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Short Questions by Mr. Akhtar Abbas @fsc:fsc_part_2_mcqs
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MATH-300: Basic Mathematics for Chemist @atiq
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Chapter 05: Partial Fractions @fsc:fsc_part_1_solutions
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Syllabus for PU @msc:syllabus
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Home
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Old Papers (FSc Part 2) @fsc
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Akhtar Abbas @people
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MTH322: Real Analysis II (Spring 2023) @atiq
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Short Term Preparation FSc 2 @fsc-part2-ptb
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Papers
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FSc Part 1 Model Papers @fsc
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Preparation Guide @msc:syllabus:uos
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MCQs with key @fsc:fsc_part_2_mcqs
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Dr. Muhammad Imran Qurshi
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MTH321: Real Analysis I (Spring 2023) @atiq
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FSc (Kyber Pakhtunkhwa (KPK) Boards) @fsc
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Complex Analysis by M Usman Hamid @notes
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Unit 07: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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Report Error
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Report Error
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MTH211: Discrete Mathematics (Fall 2020) @atiq
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Definitions: FSc Part1 KPK @fsc-part1-kpk
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Important Formulas Derivatives @fsc
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Definitions: FSc Part1 KPK @math-11-kpk
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Ch 02: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Unit 01: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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Unit 02: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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Unit 03: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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Unit 04: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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Unit 05: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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MTH211: Discrete Mathematics (Spring 2022) @atiq
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Short Term Preparation FSc 1 @fsc-part1-ptb
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Important Questions: HSSC-II @fsc-part2-ptb
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Important Formulas Integration @fsc
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Complex Analysis (Quick Review) @notes
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Model Paper FSc Part 2 @fsc:fsc_part_2_model_papers
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BISE FSc Part 2 @fsc:fsc_part_2_old_papers
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Federal Board (FSc Part 2) @fsc:fsc_part_2_old_papers
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Ch 01: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 03: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 04: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 05: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 06: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 07: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 08: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 09: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 10: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 11: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 12: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 13: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Ch 14: Key @fsc:fsc_part_1_mcqs:mcqs_by_nauman_idrees
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Unit 06: Key @fsc:fsc_part_2_mcqs:mcqs_by_nauman_idrees
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