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Question 8, Exercise 1.2
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... how that $\overline{z}=-z$ if and only if $z$ is pure imaginary. ====Solution==== Suppose that $z=a+... it in (1), we get $$z=0+bi=bi,$$ that is, $z$ is pure imaginary. Conversly, suppose that $z$ is pure imaginary, then its real part will be zero, that is
Question 1, Exercise 1.3
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... &=\dfrac{11-11i}{11}\\ \implies w&=1-i\end{align} Put value of $w$ in (i). \begin{align}z&-4(1-i)=3i\\... =6i & -2\\ \end{array}$$ \[-w=6i-2\] \[w=2-6i\] Put value of $w$ in (i).\\ \begin{align}z&+(2-6i)=3i... hline 8z & 0 & =8\\ \end{array}\\ \implies z=1$$ Put value of $z$ in (i).\\ \begin{align} &3(1)+(2+i)
Question 3 & 4, Exercise 1.3
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... tion==== Given: $$z^2+2z_1+2=0\quad \ldots (i)$$ Put the value of $z_1=-1+i$ in (i) \begin{align}L.H.... es $z_1=-1+i$ satisfied the given equation.\\ Now put $z_2=-1-i$ in (i) \begin{align} L.H.S&=(-1-i)^2+... ===Solution==== Given: $$z^2-2z+5=0 \ldots (i)$$ Put $z=1+2i$ in equaiton (i), we have \begin{align}L
Question 2, Exercise 1.3
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB... orem, $(z-a)$ is a factor of $P(z)$ iff $P(a)=0$. Put $z=-2$ \begin{align} P(-2)&=(-2)^3+6(-2)+20\\ &... eorem $(z-a)$ is a factor of $()$ iff $P(a)=0$.\\ Put $z=2$\\ \begin{align}P(-2)&=(-2)^3+6(-2)+20\\ &
Question 1, Exercise 1.1
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB
Question 2 & 3, Exercise 1.1
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB
Question 4, Exercise 1.1
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB
Question 5, Exercise 1.1
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB
Question 6, Exercise 1.1
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB
Question 7, Exercise 1.1
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB
Question 8, Exercise 1.1
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB
Question 9 & 10, Exercise 1.1
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB
Question 11, Exercise 1.1
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB
Question 1, Exercise 1.2
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB
Question 2, Exercise 1.2
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unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB
Question 3 & 4, Exercise 1.2
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Question 5, Exercise 1.2
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Question 6, Exercise 1.2
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Question 7, Exercise 1.2
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Question 9, Exercise 1.2
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Question 5, Exercise 1.3
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Question 6, Exercise 1.3
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Question 1, Review Exercise 1
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Question 2 & 3, Review Exercise 1
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Question 4 & 5, Review Exercise 1
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Question 6, 7 & 8, Review Exercise 1
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