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- Definitions: Mathematics 11 NBF
- 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 al... is usually denoted by $\mathbb{C}$. Every complex number $x+i y$ has two parts $x$ and $y$. $x$ is called ... Re(z)=x$ and $Im(z)=y$. **Conjugate of a Complex Number:** Conjugate of a complex number $z=x+i y$ is den
- Question 1, Exercise 1.4 @math-11-nbf:sol:unit01
- kistan. =====Question 1(i)===== Write a complex number $2+i 2 \sqrt{3}$ in polar form. ** Solution. ** ... ) = \frac{\pi}{3}. \end{align} Since the complex number \( 2 + i 2 \sqrt{3} \) lies in the first quadrant... ==Question 1(ii)===== Write the following complex number $3-i \sqrt{3}$ in polar form. ** Solution. ** L... &= \frac{\pi}{6}. \end{align} Since the complex number \( 3 - i \sqrt{3} \) lies in the fourth quadrant,
- Question 6(i-ix), Exercise 1.4 @math-11-nbf:sol:unit01
- =====Question 6(i)===== Write a given complex number in the algebraic form: $\sqrt{2}\left(\cos 315^{\... n} =====Question 6(ii)===== Write a given complex number in the algebraic form: $5\left(\cos 210^{\circ}+i... } =====Question 6(iii)===== Write a given complex number in the algebraic form: $2\left(\cos \dfrac{3 \pi}... *} =====Question 6(iv)===== Write a given complex number in the algebraic form: $4\left(\cos \dfrac{5 \pi}
- Question 2, Exercise 1.1 @math-11-nbf:sol:unit01
- ====Question 2(i)==== Write the following complex number in the form $x+iy$: $(3+2i)+(2+4i)$ ** Solution.... ===Question 2(ii)==== Write the following complex number in the form $x+iy$: $(4+3i)-(2+5i)$ **Solution.*... ==Question 2(iii)==== Write the following complex number in the form $x+iy$: $(4+7i)+(4-7i)$ **Solution.*... ===Question 2(iv)==== Write the following complex number in the form $x+iy$: $(2+5i)-(2-5i)$ **Solution.*
- Question 6(x-xvii), Exercise 1.4 @math-11-nbf:sol:unit01
- . =====Question 6(x)===== Write a given complex number in the algebraic form: $7 \sqrt{2}\left(\cos \dfr... // =====Question 6(xi)===== Write a given complex number in the algebraic form: $10 \sqrt{2}\left(\cos \df... =====Question 6(xii)===== Write a given complex number in the algebraic form: $2\left(\cos\dfrac{5\pi}{2... =====Question 6(xiii)===== Write a given complex number in the algebraic form: $\dfrac{1}{\sqrt{2}}\left(
- Question 18 and 19, Exercise 6.2 @math-11-nbf:sol:unit06
- n. ** We must make $4$ digit numbers to keep the number less that $10000$\\ and digit at unit place must be either $3$ or $5$ to make number odd.\\ Possible numbers starting with $0$ and end... than $10000$ using all $5$ digits$=6+6=12$\\ Odd number ending at $3$ using $4$ digits out of given $5$ digits $={ }^{4} P_{3}=2$\\ $4$ digit odd number end at $5$ using $4$ digits out of$5={ }^{4} P_{3
- MCQs: Math 11 NBF
- === Chose the correct option. i. Every real number is also a number. * (a) natural * (b) integer * %%(c)%% complex * (d) rational \\ <btn... ">%%(c)%%: complex</collapse> ii. Every complex number has $\operatorname{part}(\mathrm{s})$. * (a... >(b): two</collapse> iii. Magnitude of a complex number $z$ is the distance of $z$ from * (a) $(0,0
- Question 1, Review Exercise @math-11-nbf:sol:unit01
- === Chose the correct option. i. Every real number is also a number. * (a) natural * (b) integer * %%(c)%% complex * (d) rational \\ <btn... ">%%(c)%%: complex</collapse> ii. Every complex number has $\operatorname{part}(\mathrm{s})$. * (a... >(b): two</collapse> iii. Magnitude of a complex number $z$ is the distance of $z$ from * (a) $(0,0
- Question 4 and 5, Exercise 6.2 @math-11-nbf:sol:unit06
- digits out of given $6$ digits to make a F3-digit number.\\ To ensure the created number is even we have to choose the right most digit of number to be even.\\ Case $\mathrm{I}:$ If unit digit (right most digit) of number is $2$.\\ $$\underline{ },\underline{ },\underlin
- Question 1, Review Exercise 6 @math-11-nbf:sol:unit06
- llapsed="true">(a): $r!$</collapse> iv. The total number of $6$-digit number in which all the odd and only odd digits appear is:\\ * (a) $\dfrac{5}{2}\,\,6!$\... llapse> v. Let $A=\{1,2,3,4,...,20\}. $ Find the number of ways that the integer chosen a prime number is:\\ * (a) $3$ * (b) $5$ * %%(c)%% $7$
- Question 6(vi-ix), Exercise 6.1 @math-11-nbf:sol:unit06
- \in N$: $ (n!+1)$ is not divisible by any natural number between $2$ and $n$. ** Solution. ** We know $$... 2)\cdots 3.2.1$$ Hence $n!$ is divisible by every number between $1$ and $n$.\\ $n!$ can also divides by any natural number between $2$ and $n$.\\ For $(n!+1)$, $1$ is not divisible by any natural number between $2$ and $n$.\\ So $ (n!+1)$ is not divisi
- Question 7 and 8, Exercise 6.3 @math-11-nbf:sol:unit06
- i)===== There are $10$ points on circle. Find the number of lines? ** Solution. ** For a line, we need only two points so number of ways to choose $2$ points out of $10$ are $={ ... _{2}=45$ ( (ii) For triangle we need 3 points and number of ways to choose 3 points out of 10 are $={ }^{1... i)===== There are $10$ points on circle. Find the number of triangles that can be drawn? ** Solution. **
- Question 4, Exercise 1.1 @math-11-nbf:sol:unit01
- . ====Question 4(i)==== Find the values of real number $x$ and $y$ in each of the following: $(2+3i)x+(1... ====Question 4(ii)==== Find the values of real number $x$ and $y$ in each of the following: $\dfrac{x}{... ====Question 4(iii)==== Find the values of real number $x$ and $y$ in each of the following: $\dfrac{x}{... . ====Question 4(iv)==== Find the values of real number $x$ and $y$ in each of the following: $x(1+i)^2+y
- Question 6, Exercise 1.1 @math-11-nbf:sol:unit01
- estion 6(i)==== Find the conjugate of the complex number $4-3 i$. **Solution.** Given: $z=4-3 i$, then $... stion 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.** Given:... stion 6(iv)==== Find the conjugate of the complex number $\dfrac{5 }{2}i-\dfrac{7}{8}$. **Solution.** G
- Exercise 6.2 (Solutions) @math-11-nbf:sol:unit06
- & 5 ]] **Question 5.** How many 7 -digits mobile number can be made using the digits 0 to 9 , if each number starts with 5 and no digit is repeated?\\ [[math-11-... on: Question 10 & 11]] **Question 12.** Find the number of arrangement of letters of the word VOWEL in wh... on: Question 18 & 19]] **Question 20.** Find the number of ways that 6 men and 6 women seated at a round