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- 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}{{{
- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
- 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
- _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
- 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
- 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 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}} =... f all exercises of chapter 02==== * [[vfsc2>ch02:view&cp=01&p=07&ch=02&fp=Ex-2-1-FSC-part2-ver3|Exercise 2.1]] * [[vfsc2>ch02:view&cp=01&
- FSc
- of FBISE and BISE) given here, are useful for FSc Part 1 and Part 2 (HSSC). //Text Book of Algebra and Trigonometry C... nd //Calculus and Analytic Geometry, MATHEMATICS 12, Punjab Text Book Board Lahore// are generally used. The Notes of FSc Part 1 of “A Textbook of Mathematics For Class XI” and FSc Part 2 of “A Textbook of Mathematics For Class XII” publ... * (by Ali Nawaz Bajwa (MS(Math), M.Ed.)) 8-O ====Part 2==== * **[[FSc:FSc Part 2 Important Derivatives
- 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... t2-ver3.pdf|Download PDF]] (137KB) * Exercise 3.2 | [[vfsc2>ch03:view&cp=01&p=06&ch=03&fp=Ex-3-2-FSC-part2-ver3|View Online]] | [[pdf>files/fsc/fsc_part2/ch03/dn.php?file=Ex-3-2-FSC-part2-ver3.pdf|Download PDF]] (186KB) * Exercise 3
- FSc Part 1 (KPK Boards) @fsc
- math-11-kpk|AVAILABLE HERE]] </text> {{ :fsc:fsc-part-1-kptb.jpg?nolink&600x315|FSc Part 2 KPTP}} Notes of FSc Part 1 of "A Textbook of Math... success" icon="fa fa-download"> **{{:fsc:kpk_fsc_part_1:ch02-matrices-and-determinants-fsc1-kpk.pdf|Download PDF}}** | **[[:fsc:kpk fsc part 1:chapter 02 matrices and determinants|View Online]]** </callo... "success" icon="fa fa-download"> **{{:fsc:kpk_fsc_part_1:ch12-graph-of-trigonometric-and-inverse-trigonometric-
- FSc/ICS Part 2 Solutions @fsc
- ====== FSc/ICS Part 2 Solutions ====== {{ :fsc:fsc-math-part2.jpg?nolink|Calculus and Analytic Geometry, MATHEMATICS 12}} <lead>Notes (Solutions) of Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc/ICS Part 2 or HSSC-II), Punjab Text Book Board Lahore.</le... to view PDF on their smartphone. * **[[FSc:FSc Part 2 Solutions:ch01]]** * **[[FSc:FSc Part 2 Solu
- 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 8, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- ==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit01:ex1-2-p6|< Question 7]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-2-p8|Question 9 >]]</btn></text>
- Question 8, Exercise 1.2 @math-11-kpk:sol:unit01
- ====== Question 8, Exercise 1.2 ====== Solutions of Question 8 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of A Textbo... ====Question 8(i)===== Show that $z+\overline{z}=2\operatorname{Re}\left( z \right)$. ====Solution==... ib \right)\\ &=a+ib+a-ib\\ &=2a\\ z+\overline{z}&=2\operatorname{Re}\left( z \right)\end{align} ====
- Chapter 09: Fundamentals of Trigonometry @fsc:fsc_part_1_solutions
- c-part1-ver3-1.pdf |Download PDF}} * Exercise 9.2 | [[vfsc1>ch09:view&cp=01&p=06&ch=09&fp=Ex-9-2-FSC-part1-ver3-1|View Online]] | {{ :fsc:fsc_part_1_solutions:ex-9-2-fsc-part1-ver3-1.pdf |Download PDF}} * Exercise 9.3 | [[vfsc... htar-abbas.pdf |Download PDF}} NEW * Exercise 9.2 | {{ :fsc:fsc_part_1_solutions:ex-9-2-fsc-part1-akhtar-abbas.pdf |Download PDF}} NEW * Exercise 9.3 | {{ :fsc:fsc_part_1_solutions:ex-9-3-fsc-part1-akhtar-abbas.pdf |Do