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- Question 9, Exercise 1.2
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. ====Question 9(i... =3-2i$. We will use the following formulas: \[\text{Re}(z^{-2}) = \frac{(\text{Re}(z))^2 - (\text{Im}(z))^2}{|z|^4},\] \[\text{Im}(z^{-2}) = \frac{-2 \text
- Question 2, Exercise 1.2
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. ====Question 2==... ign} &(z_1 z_2)(z_3 z_4) \\ =&(z_1 z_2)z_5 \quad \text {Let }z_5=z_3 z_4 \\ =&z_1 (z_2 z_5) \quad \text{Multiplicative assocative law}\\ =&z_1\left(z_2 (z_3 z
- Question 3, Exercise 1.2
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. ====Question 3(i... f $z=\bar{z}$. **Solution.** Let $$z=a+ib\quad \text{where}\quad a,b\in \mathbb{R}\, ... (1)$$ First s... $z$ is real or pure imaginary, then $$z=x \quad \text{ or } \quad z=iy.$$ This gives $$\bar{z}=x \quad
- Question 3, Exercise 1.4
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. =====Question 3... \begin{align*} &|z_r|=\sqrt{x_r^2+y_r^2} \quad \text{and}\quad |z|=\sqrt{a^2+b^2}. \\ &\theta_k = \arg... ) = \tan^{-1}\left(\dfrac{y_r}{x_r}\right) \quad \text{and}\quad \theta=\tan^{-1}\left(\dfrac{b}{a}\righ
- Question 5, Exercise 1.1
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. ====Question 5==... real and imaginary parts. \begin{align}x=4 \quad \text{and}\quad 7y &=-7 \,\text{ i.e. }\,y=-1.\end{align} Thus we have $z=x+iy=4-i$. GOOD ====Go to ==== <t
- Question 9, Exercise 1.4
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. =====Question 9... \neq 1.$$ <fc #ff0000>The contents, given in the textbook, related to these question are not suffient t... ution. ** <fc #ff0000>The contents, given in the textbook, related to these question are not suffient t
- Question 5, Exercise 1.2
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. ====Question 5==... *Solution.** Suppose \begin{align}z_1&=x_1+iy_1 \text{ and } z_2&=x_2+iy_2\end{align} Now \begin{align}... (z_2)+4Im(z_1)Im(z_2).\end{align} ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:so
- Question 6, Exercise 1.2
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. ====Question 6==... **Solution.** Given: \begin{align} &z_{1}=3+i\text{ and } z_{2}=1+i.\end{align} Now \begin{align} \... {-3\pm i\sqrt{3}}{2} \end{align} ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:so
- Question 3, Exercise 1.3
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. ====Question 3(... 4ac}}}}{2a},$$ where $$a = 1,\quad b = 6,\quad \text{and}\quad c = -48.$$ Then \begin{align} z& = \d... ac{9 \pm \sqrt{37}}{2}\right\}$ ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:so
- Question 7, Exercise 1.4
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. =====Question 7... 1-z) \\ = & \arg(1-i(x+iy))-\arg(1-(x+iy)) \quad \text{ as } z=x+iy \\ = & \arg(1-ix-i^2y)-\arg(1-x-iy) ... xy=0. \end{align*} As required. ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:so
- Question 2, Exercise 1.1
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. ====Question 2(... frac{3}{13}i.\\ \end{align} GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit01:ex1-1-p1|< Question 1]]</btn></text> <text align="right"><btn type="success">[[math-1
- Question 3, Exercise 1.1
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. ====Question 3(i... }{5}\\ =&5+i. \end{align} GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit01:ex1-1-p2|< Question 2]]</btn></text> <text align="right"><btn type="success">[[math-1
- Question 4, Exercise 1.1
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. ====Question 4(i... +10i\end{align} Now do yourself ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit01:ex1-1-p3|< Question 3]]</btn></text> <text align="right"><btn type="success">[[math-1
- Question 6, Exercise 1.1
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. ====Question 6(i... ac{5 }{2}i-\dfrac{7}{8}$. GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit01:ex1-1-p5|< Question 5]]</btn></text> <text align="right"><btn type="success">[[math-1
- Question 4, Exercise 1.2
- f Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. ====Question 4=... c{16}{\sqrt{13}}\end{align} GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit01:ex1-2-p3|< Question 3]]</btn></text> <text align="right"><btn type="success">[[math-1