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- Question 4, Exercise 1.3
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... 3i \quad\cdots(2) \end{align} Multiplying Eq. (1) by $2$: \begin{align} &(2-2i)z+(2+2i) \omega=6 \quad \cdots (3) \end{align} Multiplying Eq. (2) by $(1-i)$: \begin{align} &2(1-i)z-(1-i) (2+5 i)\ome... i \quad \cdots(2) \end{align} Multiplying $(1)$ by $(1-2i)$, we get: \begin{align} &(1-2i)(2i z) +
- Question 8, Exercise 1.2
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... (i)==== Write $|2 z-i|=4$ in terms of $x$ and $y$ by taking $z=x+i y$. **Solution.** Given: $$|2z-i... Write $|z-1|=|\bar{z}+i|$ in terms of $x$ and $y$ by taking $z=x+i y$. **Solution.** Given: $$|z-1|=... rite $|z-4 i|+|z+4 i|=10$ in terms of $x$ and $y$ by taking $z=x+i y$. **Solution.** Given: $$|z-4i
- Question 1, Exercise 1.3
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... z+\dfrac{3}{2}$ is the factor of polynomial. Then by using synthetic division: \begin{align} \begin{ar... So $z-(1)=z-1$ is the factor of polynomial. Then by using synthetic division: \begin{align} \begin{ar... So $z-(-3)=z+3$ is the factor of polynomial. Then by using synthetic division: Now, by synthetic divis
- Question 2, Exercise 1.3
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... istan. ====Question 2(i)==== Solve the equation by completing square: $z^{2}-6 z+2=0$. **Solution.*... }\}$. ====Question 2(ii)==== Solve the equation by completing square: $-\dfrac{1}{2} z^{2}-5 z+2=0$.... z^{2} - 5z + 2& = 0 \end{align} Multiply through by $-2$ to eliminate the fraction: \begin{align} z^2
- Question 8, Exercise 1.4
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... $$x_{\max}=0.004, \quad \theta=\dfrac{\pi}{4}.$$ By using the formula \begin{align} x&=x_{\max} e^{i\... $$x_{\max}=0.004, \quad \theta=\dfrac{\pi}{3}.$$ By using the formula \begin{align} x &= x_{\max} e^{... $$x_{\max}=0.004, \quad \theta=\dfrac{\pi}{6}.$$ By using the formula \begin{align} x &= x_{\max} e^{
- Question 6, Exercise 1.2
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... \\ \implies &\lambda^2+3\lambda+3=0. \end{align} By using quadratic formula, we have \begin{align} \
- Question 3, Exercise 1.4
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... \cdot z_2 \cdot z_3 \cdots z_n = z. \end{align*} By using $(1)$, we have \begin{align*} &|z_1| e^{i\t
- Question 9, Exercise 1.4
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... n. ** Here we have $$x=2+3i$$ $$x_{\max}=1+4 i$$ By using the formula $$\implies x=x_{\max} e^{i\thet
- Question 7, Review Exercise
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... lamabad, Pakistan. ===== Question 7 ===== Solve by completing square method $2 z^{2}-11 z+16=0$. *
- Question 8, Review Exercise
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... eta=\dfrac{\pi}{4}.$$ We have to find $x_{\max}$. By using the formula \begin{align} &x=x_{\max} e^{i\
- Question 1, Exercise 1.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo
- Question 2, Exercise 1.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo
- Question 3, Exercise 1.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo
- Question 4, Exercise 1.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo
- Question 5, Exercise 1.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo