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- Exercise 2.6 (Solutions) @matric:9th_science:unit_02
- 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
- 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
- Unit 02: Differentiation @fsc:fsc_part_2_solutions
- ===== 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 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- 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
- 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}
- Unit 02: Matrices and Determinants (Solutions) @math-11-kpk:sol
- ===== Unit 02: Matrices and Determinants (Solutions) ===== This is a second unit of the book Mathema... bers and $i=\sqrt{-1}$. * Recognize $a$ as real part of $z$ and $b$ as imaginary part of $z$. * Know condition for equality of complex numbers. * Carry ... conjugate of $z=a+ib$. * Define $|z| = \sqrt{a^2+b^2}$ as the absolute value or modulus of a compl
- Question 7, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- =&\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
- =&\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: Mathematics FSc part 2 @fsc:fsc_part_2_solutions:ch02
- ====== Unit 02: Differentiation: Mathematics FSc part 2 ====== Notes (Solutions) of Unit 02: Differentiation, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. The... hapter for MCQs and important question [[:fsc:fsc_part_1_solutions:ch02|here]]. {{include>fsc_part2_viewer_new.php}} ====Here is the list of all exercises of chapter 02====
- Chapter 02: Sets, Functions and Groups @fsc:fsc_part_1_solutions
- -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
- has been given below this preview. {{include>fsc_part2_viewer_new.php}} ====Here is the list of 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=
- Chapter 12: Application of Trigonometry @fsc:fsc_part_1_solutions
- 2: Application of Trigonometry ====== {{ :fsc:fsc_part_1_solutions:fsc-1-chap-12-ptb.jpg?nolink|Chapter 12: Application of Trigonometry}} Notes (Solutions) ... ype="success" icon="fa fa-download"> * Chapter 12: Proofs of Formulas | {{ :fsc:fsc_part_1_solutions:ch12-formula-proofs-fsc-part1.pdf |Download PDF}} by Mirza Ahmad Younas NEW * Exercise 12.1 | [[vfsc1>ch12:view&cp=01&p=01&ch=12&fp=Ex-12-1-FSC-part1-ver1|View Online]] | {{ :fsc:fsc_part_1_solution
- Unit 03: Integration @fsc:fsc_part_2_solutions
- ====== Unit 03: Integration ====== {{ :fsc:fsc_part_2_solutions:fsc-2-unit-03-ptb.jpg?nolink|Unit 03: Integration}} Notes ... ion, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You... " icon="fa fa-download"> * Exercise 3.1 | [[vfsc2>ch03:view&cp=01&p=03&ch=03&fp=Ex-3-1-FSC-part2-ver3|View Online]] | [[pdf>files/fsc/fsc_part2/ch03/dn.php?file=Ex-3-1-FSC-part2-ver3.pdf|Download PDF]] (137KB) * Exercise 3.2 | [[vfsc2>ch03:
- Unit 06: Conic Section @fsc:fsc_part_2_solutions
- ====== 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-FSC-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_solutio
- Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
- 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 unde
- Unit 05: Linear Inequalities and Linear Programming: Mathematics FSc part 2 @fsc:fsc_part_2_solutions:ch05
- Ch 07: Permutation, Combination and Probability: Mathematics FSc Part 1 @fsc:fsc_part_1_solutions:ch07
- Syllabus & Paper Pattern for General Mathematics (Split Program) @bsc:paper_pattern:punjab_university
- Ch 08: Mathematical Induction and Binomial Theorem: Mathematics FSc Part 1 @fsc:fsc_part_1_solutions:ch08