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- Definitions: Mathematics 11 NBF
- page in PDF. </callout> =====Chapter 01===== **Complex Number:** A complex number is an expression of the form $x+iy$, where $x,y\in\mathbb{R}$ and $i^2=1$. Set of all complex numbers is usually denoted by $\mathbb{C}$. Every complex number $x+i y$ has two parts $x$ and $y$. $x$ is
- Unit 01: Complex Numbers (Solutions) @math-11-nbf:sol
- ===== Unit 01: Complex Numbers (Solutions) ===== This is a first unit of the book Model Textbook of Mathem... his unit the students will be able to * Recall complex number $z$ and recognize its real and imaginary part. * Know the condition for equality of two complex numbers. * Revising the basic operations on complex numbers. * Find conjugate and modulus of a complex
- Question 1, Exercise 1.4 @math-11-nbf:sol:unit01
- lutions of Question 1 of Exercise 1.4 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathem... abad, Pakistan. =====Question 1(i)===== Write a complex number $2+i 2 \sqrt{3}$ in polar form. ** Soluti... \sqrt{3}) = \frac{\pi}{3}. \end{align} Since the complex number \( 2 + i 2 \sqrt{3} \) lies in the first q... OOD =====Question 1(ii)===== Write the following complex number $3-i \sqrt{3}$ in polar form. ** Solution
- Question 6(i-ix), Exercise 1.4 @math-11-nbf:sol:unit01
- s of Question 6(i-ix) of Exercise 1.4 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathem... akistan. =====Question 6(i)===== Write a given complex number in the algebraic form: $\sqrt{2}\left(\cos... end{align} =====Question 6(ii)===== Write a given complex number in the algebraic form: $5\left(\cos 210^{\... d{align*} =====Question 6(iii)===== Write a given complex number in the algebraic form: $2\left(\cos \dfrac
- Question 2, Exercise 1.1 @math-11-nbf:sol:unit01
- lutions of Question 2 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathem... stan. ====Question 2(i)==== Write the following complex number in the form $x+iy$: $(3+2i)+(2+4i)$ ** So... GOOD ====Question 2(ii)==== Write the following complex number in the form $x+iy$: $(4+3i)-(2+5i)$ **Sol... GOOD ====Question 2(iii)==== Write the following complex number in the form $x+iy$: $(4+7i)+(4-7i)$ **Sol
- Question 6(x-xvii), Exercise 1.4 @math-11-nbf:sol:unit01
- of Question 6(x-xvii) of Exercise 1.4 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathem... Pakistan. =====Question 6(x)===== Write a given complex number in the algebraic form: $7 \sqrt{2}\left(\c... s parts.// =====Question 6(xi)===== Write a given complex number in the algebraic form: $10 \sqrt{2}\left(\... parts.// =====Question 6(xii)===== Write a given complex number in the algebraic form: $2\left(\cos\dfrac{
- MCQs: Math 11 NBF
- Textbook Board Islamabad. </lead> ===== Unit 01: Complex Numbers ===== Chose the correct option. i. ... * (a) natural * (b) integer * %%(c)%% complex * (d) rational \\ <btn type="link" collapse="... </btn><collapse id="a1" collapsed="true">%%(c)%%: complex</collapse> ii. Every complex number has $\operatorname{part}(\mathrm{s})$. * (a) one * (b) t
- Question 1, Review Exercise @math-11-nbf:sol:unit01
- ions of Question 1 of Review Exercise of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathem... * (a) natural * (b) integer * %%(c)%% complex * (d) rational \\ <btn type="link" collapse="... </btn><collapse id="a1" collapsed="true">%%(c)%%: complex</collapse> ii. Every complex number has $\operatorname{part}(\mathrm{s})$. * (a) one * (b) t
- Question 6, Exercise 1.1 @math-11-nbf:sol:unit01
- lutions of Question 6 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathem... ====Question 6(i)==== Find the conjugate of the complex number $4-3 i$. **Solution.** Given: $z=4-3 i$,... ====Question 6(ii)==== Find the conjugate of the complex number $3 i+8$. **Solution.** Do Yourself ====Question 6(iii)==== Find the conjugate of the complex number $2+\sqrt{\dfrac{-1}{5}}$. **Solution.**
- Exercise 1.2 (Solutions) @math-11-nbf:sol:unit01
- he question related to real and imaginary part of complex numbers, modulus and conjugate of the complex numbers. **Question 1.** Show that for any complex number :\\ (i) $\operatorname{Re}(i z)=-\operatorname{... **Question 2.** Use the algebraic properties of complex numbers to prove that $$\left(z_{1} z_{2}\right)\
- Question 2, Exercise 1.2 @math-11-nbf:sol:unit01
- lutions of Question 2 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathem... ===Question 2==== Use the algebraic properties of complex numbers to prove that $$ \left(z_{1} z_{2}\right)... e the required result. **Remark:** For any three complex numbers $z_1$, $z_2$ and $z_3$, we have $$z_1 (z_... ells us that the order in which we multiply three complex numbers doesn't matter; we will always end up wit
- Question 4, Exercise 1.3 @math-11-nbf:sol:unit01
- lutions of Question 4 of Exercise 1.3 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathem... e the simultaneous system of linear equation with complex coefficients: $(1-i) z+(1+i) \omega=3 ; 2 z-(2+5 ... e the simultaneous system of linear equation with complex coefficients: $2 i z+(3-2 i) \omega=1+i ;(1-2 i) ... e the simultaneous system of linear equation with complex coefficients: $\dfrac{3}{i} z-(6+2 i) \omega=5 ;
- Exercise 1.4 (Solutions) @math-11-nbf:sol:unit01
- ists of the question related to polar form of the complex numbers. **Question 1.** Write the following complex number in polar form.\\ (i) $2+i 2 \sqrt{3}$\\ (ii)... Question 1]] **Question 2.** Write the following complex number in rectangular form.\\ (i) $\left(\cos \df... tion 5]] **Question 6.** Write a following given complex number in the algebraic form:\\ (i) $\sqrt{2}\lef
- Exercise 1.1 (Solutions) @math-11-nbf:sol:unit01
- stion related to sum, product and division of the complex numbers. **Question 1.** Evaluate :\\ (i) ${{i}^... Question 1]] **Question 2.** Write the following complex number in the form $x+iy$:\\ (i) $(3+2i)+(2+4i)$ ... |Solution: Question 4]] **Question 5.** Find the complex number $z$ if $4z-3\bar{z}=\dfrac{1-18i}{2-i}$\\ ... Question 6.** Find the conjugate of the following complex number :\\ (i) $4-3 i$ (ii) $3 i+8$ (iii) $2+\sqr
- Question 1, Exercise 1.2 @math-11-nbf:sol:unit01
- lutions of Question 1 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathem... akistan. ====Question 1(i)==== Show that for any complex number, $\operatorname{Re}(i z)=-\operatorname{Im... {align} ====Question 1(ii)==== Show that for any complex number, $\operatorname{Im}(i z)=\operatorname{Re}