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- Question 2, Exercise 1.1 @math-11-nbf:sol:unit01
- abad, Pakistan. ====Question 2(i)==== Write the following complex number in the form $x+iy$: $(3+2i)+(2+4i)... end{align} GOOD ====Question 2(ii)==== Write the following complex number in the form $x+iy$: $(4+3i)-(2+5i)... end{align} GOOD ====Question 2(iii)==== Write the following complex number in the form $x+iy$: $(4+7i)+(4-7i)... end{align} GOOD ====Question 2(iv)==== Write the following complex number in the form $x+iy$: $(2+5i)-(2-5i)
- Exercise 1.4 (Solutions) @math-11-nbf:sol:unit01
- the complex numbers. **Question 1.** Write the following complex number in polar form.\\ (i) $2+i 2 \sqrt{... Solution: Question 1]] **Question 2.** Write the following complex number in rectangular form.\\ (i) $\left(... 5|Solution: Question 5]] **Question 6.** Write a following given complex number in the algebraic form:\\ (i)... tion: Question 6(i-ix)]] **Question 6.** Write a following given complex number in the algebraic form:\\ (x)
- Question 7, Exercise 1.4 @math-11-nbf:sol:unit01
- , Pakistan. =====Question 7(i)===== Convert the following equation in Cartesian form: $\arg (z-1)=-\dfrac{\... s required. =====Question 7(ii)===== Convert the following equations and inequations in Cartesian form: $z \... end{align*} =====Question 7(iii)===== Convert the following equations and inequations in Cartesian form: $-\... As required. =====Question 7(iv)===== Convert the following equations and inequations in Cartesian form: $0 \
- Question 1, Exercise 2.1 @math-11-nbf:sol:unit02
- ===== Question 1(i) ===== Find the order of the following matrix $A=\left[\begin{array}{lll}1 & 3 & 0 \\ 2 ... ===== Question 1(ii) ===== Find the order of the following matrix $B=\left[\begin{array}{ll}1 & 2 \\ 2 & 3 \... ===== Question 1(iii)===== Find the order of the following matrix $C=\left[\begin{array}{l}1 \\ 6 \\ 9\end{a... ===== Question 1(iv) ===== Find the order of the following matrix $D=\left[\begin{array}{llll}2 & 1 & 6 & 8\
- Question 2, Exercise 2.1 @math-11-nbf:sol:unit02
- Pakistan. =====Question 1(i)===== Identify the following matrix $\quad A=\left[\begin{array}{lll}3 & 6 & 2... lar matrix =====Question 1(ii)===== Identify the following matrix $B=\left[\begin{array}{ll}\frac{1}{3} & 1 ... matrix =====Question 1(iii)===== Identify the following matrix $C=\left[\begin{array}{l}3 \\ 2 \\ 8\end{a... mn matrix =====Question 1(iv)===== Identify the following matrix $D=\left[\begin{array}{lll}1 & 6 & 9 \\ 2
- Question 4, Exercise 2.1 @math-11-nbf:sol:unit02
- =====Question 4(i)===== Find the transpose of the following matrix and identify which one is symmetric and wh... ====Question 4(ii)===== Find the transpose of the following matrix and identify which one is symmetric and wh... ===Question 4(iii)===== Find the transpose of the following matrix and identify which one is symmetric and wh... ====Question 4(iv)===== Find the transpose of the following matrix and identify which one is symmetric and wh
- Exercise 6.1 (Solutions) @math-11-nbf:sol:unit06
- ight. $$ </callout> **Question 1.** Evaluate the following:\\ (i) $10!$ (ii) $\dfrac{12!}{7! 3! 2!}$ (iii) $... Solution: Question 1]] **Question 2.** Write the following in factorial form:\\ (i) 14.13 .12 .11 (ii) 1.3.5... olution: Question 2 ]] **Question 3.** Prove the following:\\ (i) $\frac{1}{5!}+\frac{3}{6!}+\frac{1}{7!}=\f... ]] **Question 5.** Find the values of $n$ in the following.\\ (i) $\frac{n}{(n-4)!}=\frac{3.3!}{(n-3)!}$ (ii
- Exercise 1.1 (Solutions) @math-11-nbf:sol:unit01
- Solution: Question 1]] **Question 2.** Write the following complex number in the form $x+iy$:\\ (i) $(3+2i)+... ution: Question 2]] **Question 3.** Simplify the following :\\ (i) $\dfrac{(2+i)(3-2i)}{1+i}$ (ii) $\dfrac{1... values of real number $x$ and $y$ in each of the following:\\ (i) $(2+3i)x+(1+3i)y+2=0$ (ii) $\dfrac{x}{(1+i... on 5]] **Question 6.** Find the conjugate of the following complex number :\\ (i) $4-3 i$ (ii) $3 i+8$ (iii)
- Exercise 2.3 (Solutions) @math-11-nbf:sol:unit02
- **Question. 1** Evaluate the determinant of the following matrices.\\ (i) $\left[\begin{array}{ccc}2 & 3 &... **Question. 2** Evaluate the determinants of the following matrices using cofactor method.\\ (i) $\left[\be... stion 2]] **Question. 3** Determine which of the following matrices are singular and which are non-singular.... stion. 5** Find the multiplicative inverse of the following matrices if it exists by adjoint method.\\ (i) $
- Question 3, Exercise 1.1 @math-11-nbf:sol:unit01
- ad, Pakistan. ====Question 3(i)==== Simplify the following $\dfrac{(2+i)(3-2i)}{1+i}$ **Solution.** \begin{... d{align} GOOD ====Question 3(ii)==== Simplify the following $\dfrac{1+i}{(2+i)^2}$ **Solution.** \begin{ali... align} GOOD ====Question 3(iii)==== Simplify the following $\dfrac{1}{3+i}-\dfrac{1}{3-i}$ **Solution.** \... d{align} GOOD ====Question 3(iv)==== Simplify the following $(1+i)^{-2}+(1-i)^{-2}$ **Solution.** \begin{al
- Question 4, Exercise 1.1 @math-11-nbf:sol:unit01
- values of real number $x$ and $y$ in each of the following: $(2+3i)x+(1+3i)y+2=0$ **Solution.** \begin{al... values of real number $x$ and $y$ in each of the following: $\dfrac{x}{(1+i)}+\dfrac{y}{1-2i}=1$ **Solution... values of real number $x$ and $y$ in each of the following: $\dfrac{x}{(2+i)}=\dfrac{1-5i}{(3-2i)}+\dfrac{y}... values of real number $x$ and $y$ in each of the following: $x(1+i)^2+y(2-i)^2=3+10i$ **Solution.** \begi
- Question 9, Exercise 1.2 @math-11-nbf:sol:unit01
- Suppose $z=3 - \sqrt{-4}=3-2i$. We will use the following formulas: \[\text{Re}(z^{-2}) = \frac{(\text{Re}... i}{3-i}\right)^{-1}$. **Solution.** We use the following formulas: \[Re\left(\left(\frac{x_1 + i y_1}{x_... i}\right)^{-2}$. **Solution.** We will use the following formulas: \begin{align} &Re\left(\left(\frac{x_... i}\right)^{2}$. **Solution.** We will use the following formulas: \[\text{Re}\left(\left(\frac{x_1 + i
- Exercise 1.3 (Solutions) @math-11-nbf:sol:unit01
- e complex numbers. **Question 1.** Factorize the following polynomial into linear functions:\\ (i) $z^{2}+16... Solution: Question 1]] **Question 2.** Solve the following equation by completing square:\\ (i) $z^{2}-6 z+2... Solution: Question 2]] **Question 3.** Solve the following quadratic equation:\\ (i) $\dfrac{1}{3} z^{2}+2 z... Solution: Question 3]] **Question 4.** Solve the following simultaneous system of linear equation with compl
- Question 2, Review Exercise @math-11-nbf:sol:unit01
- ===== Question 2(i) ===== Find the value of the following: $i^{2}+i^{4}+i^{6}+\cdots+i^{100}$\\ ** Solutio... ===== Question 2(ii) ===== Find the value of the following: $\left|\dfrac{(3-2 i)(1+i)}{2-3 i}\right|$ ** S... ==== Question 2(iii) ===== Find the value of the following: $|\overline{(3-2 i)(4-i)}|$ ** Solution. ** \b... ===== Question 2(iv) ===== Find the value of the following: $\left(\dfrac{3+5 i}{2-3 i}\right)^{-1}$ ** So
- Question 2, Exercise 2.3 @math-11-nbf:sol:unit02
- estion 2(i)===== Evaluate the determinant of the following matrix $\left[\begin{array}{lll}3 & 2 & 3 \\ 4 & ... stion 2(ii)===== Evaluate the determinant of the following matrix $\left[\begin{array}{ccc}2 & 3 & -1 \\ -1 ... tion 2(iii)===== Evaluate the determinant of the following matrix $\left[\begin{array}{ccc}2 i & 6 & 1 \\ 1 ... stion 2(iv)===== Evaluate the determinant of the following matrix $\left[\begin{array}{ccc}1-i & 2 & 1+i \\