This is beta site. https://beta.mathcity.org/ 2026-06-06T20:39:41+00:00 https://beta.mathcity.org/ https://beta.mathcity.org/_media/logo.png text/html 2025-01-21T16:13:57+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/math-11-kpk/sol/unit01/review-ex-1-p2?rev=1737476037&do=diff Question 2 & 3, Review Exercise 1 Solutions of Question 2 & 3 of Review Exercise 1 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.${{i}^{n}}+{{i}^{n+1}}+{{i}^{n+2}}+{{i}^{n+3}}=0$$\forall n\in N$\begin{align}{{i}^{n}}+{{i}^{n+1}}+{{i}^{n+2}}+{{i}^{n+3}}&=0\\ L.H.S.&={{i}^{n}}+{{i}^{n}}\cdot i+{{i}^{n}}\cdot {{i}^{2}}+{{i}^{n}}\cdot {{i}^{3}}\\ &={{i}^{n}}\left( 1+i+{{i}^{2}}… text/html 2025-01-21T16:13:57+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/math-11-kpk/sol/unit01/review-ex-1-p3?rev=1737476037&do=diff Question 4 & 5, Review Exercise 1 Solutions of Question 4 & 5 of Review Exercise 1 of Unit 01: Complex Numbers. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.${{z}_{1}}=2-i$${{z}_{2}}=1+i,$$\left|\dfrac{{{z}_{1}}+{{z}_{2}}+1}{{{z}_{1}}-{{z}_{2}}+1}\right|$$z_1=2-i$$z_2=1+i$\begin{align} \dfrac{{{z}_{1}}+{{z}_{2}}+1}{{{z}_{1}}-{{z}_{2}}+1}&=\dfrac{\left( 2-i \right)+\left( 1+i \right)+1}{\left( 2-i \rig… text/html 2025-01-21T16:13:57+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/math-11-kpk/sol/unit01/review-ex-1-p1?rev=1737476037&do=diff Question 1, Review Exercise 1 Solutions of Question 1 of Review Exercise 1 of Unit 01: Complex Numbers. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. Question 1 ${{\left( \dfrac{2i}{1+i} \right)}^{2}}$$i$$2i$$1-i$$i+1$$\dfrac{5+2i}{4-3i}$$-\dfrac{7}{25}+\dfrac{26}{25}i$$\dfrac{5}{4}-\dfrac{2}{3}i$$\dfrac{14}{25}+\dfrac{23}{25}i$$\dfrac{26}{7}+\dfrac{23}{7}i$${{i}^{57}}+\frac{1}{{{i}^{25}}}$$0$$2i$$-2… text/html 2025-01-21T16:13:57+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/math-11-kpk/sol/unit01/review-ex-1-p4?rev=1737476037&do=diff Question 6, 7 & 8, Review Exercise 1 Solutions of Question 6, 7 & 8 of Review Exercise 1 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.$\dfrac{1}{3+4i}$$$z=\dfrac{1}{3+4i}.$$\begin{align}z&=\dfrac{1}{3+4i}\times \dfrac{3-4i}{3-4i}\\ &=\dfrac{3-4i}{9+16}\\ &=\dfrac{3-4i}{25}\\ &=\dfrac{3}{25}-\dfrac{4}{25}i\end{align}$$\bar{z}=\dfrac{3}{25}+\dfrac{4}{25}i.$$$\dfrac{3i+2}{3-2…