Merging man & maths https://www.mathcity.org/ Thu, 04 Jun 2026 07:24:31 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/math-11-kpk/sol/unit01/ex1-3-p2 Question 2, Exercise 1.3 Solutions of Question 2 of Exercise 1.3 of Unit 01: Complex Numbers. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. Question 2(i) $P(z)$$$P\left( z \right)={{z}^{3}}+6z+20$$$$p\left( z \right)={{z}^{3}}+6z+20$$$(z-a)$$P(z)$$P(a)=0$$z=-2$\begin{align} P(-2)&=(-2)^3+6(-2)+20\\ &=-8-12+20\\ &=0\end{align}$z+2$${{z}^{3}}+6z+20$$$\begin{array}{c|cccc} -2 & 1 & 0 & 6 & 20 \\ & \d… anonymous@undisclosed.example.com (Anonymous) Tue, 05 Dec 2023 02:45:02 +0000 https://www.mathcity.org/math-11-kpk/sol/unit01/ex1-3-p1 Question 1, Exercise 1.3 Solutions of Question 1 of Exercise 1.3 of Unit 01: Complex Numbers. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. Question 1(i) \begin{align}&z-4w=3i\\ &2z+3w=11-5i\end{align}\begin{align}z-4w&=3i …(i)\\ 2z+3w&=11-5i …(ii)\end{align}$2$\begin{align}2z-8w&=6i …(iii)\end{align}\[\begin{array}{cccc} 2z&-8w&=6i \\ \mathop+\limits_{-}2z&\mathop+\limits_{-}3w&=\mathop-\limit… anonymous@undisclosed.example.com (Anonymous) Tue, 05 Dec 2023 02:45:01 +0000 https://www.mathcity.org/math-11-kpk/sol/unit01 Unit 01: Complex Numbers (Solutions) This is a first unit of the book Mathematics 11 published by Khyber Pakhtunkhwa Textbook Board, Peshawar, Pakistan. On this page we have provided the solutions of the questions. After reading this unit the students will be able to$z$$z=a+ib$$(a,b)$$a$$b$$i=\sqrt{-1}$$a$$z$$b$$z$$\bar{z} = a —ib$$z=a+ib$$|z| = \sqrt{a^2+b^2}$$z=a+ib$$'+'$$'\times'$$z$$|z|=|-z|=|\bar{z}=|-\bar{z}|$$pz^2+ qz+ r = 0$$p,q,r$$z$ anonymous@undisclosed.example.com (Anonymous) Thu, 01 Feb 2024 02:28:42 +0000 https://www.mathcity.org/math-11-kpk/sol/unit02 Unit 02: Matrices and Determinants (Solutions) This is a second unit of the book Mathematics 11 published by Khyber Pakhtunkhwa Textbook Board, Peshawar, Pakistan. On this page we have provided the solutions of the questions. After reading this unit the students will be able to$z$$z=a+ib$$(a,b)$$a$$b$$i=\sqrt{-1}$$a$$z$$b$$z$$\bar{z} = a —ib$$z=a+ib$$|z| = \sqrt{a^2+b^2}$$z=a+ib$$'+'$$'\times'$$z$$|z|=|-z|=|\bar{z}=|-\bar{z}|$$pz^2+ qz+ r = 0$$p,q,r$$z$ anonymous@undisclosed.example.com (Anonymous) Tue, 05 Dec 2023 02:44:47 +0000 https://www.mathcity.org/math-11-kpk/sol/unit06/ex6-3-p5 Question 5 and 6 Exercise 6.3 Solutions of Question 5 and 6 of Exercise 6.3 of Unit 06: Permutation, Combination and Probablity. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.$12$$n=12$${ }^{12} C_2=66$$12$$n=12$${ }^{12} C_3=220$$${ }^6 C_2=\dfrac{6 !}{(6-2) ! 2 !}=15 $$$6$$\quad 15-6=9$ anonymous@undisclosed.example.com (Anonymous) Thu, 01 Feb 2024 02:35:46 +0000