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- Question 10, Exercise 1.2 @math-11-nbf:sol:unit01
- = \sqrt{13}.$$ As required. GOOD ====Question 10(ii)==== For $z_{1}=-3+2 i$ and $z_{2}=1-3 i$ verify:... ne{z_2}} = -\frac{9}{10} + \frac{7}{10}i.\,\, -- (ii)$$ From (i) and (ii), we have \[ \overline{\left( \frac{z_1}{z_2} \right)} = \frac{\overline{z_1}}{\overline{z_2}}. \] GOOD ====Question 10(iii)==== For $z_{1}=-3+2 i$ and $z_{2}=1-3 i$ verify
- Question 1, Exercise 2.6 @math-11-nbf:sol:unit02
- {3}=0\cdots (i)\\ &x_{1}-2 x_{2}+3 x_{3}=0\cdots (ii)\\ &4 x_{1}+x_{2}-6 x_{3}=0\cdots (iii)\\ \end{align*} For system of equation, \begin{align*} A &= \... m has non-trivial solution. \text{By}\quad(i)-2(ii), we have \begin{align*} &\begin{array}{cccc} 2x_... 2=2x_3\\ \end{align*} Put the value of $x_3$ in (iii), we have \begin{align*} &4 x_{1}+2x_{3}-6 x_{3}
- Question 2, Exercise 2.6 @math-11-nbf:sol:unit02
- _{3}=0 \cdots(i)\\ &2 x_{1}+3 x_{2}-x_{3}=0\cdots(ii)\\ &3 x_{1}-2 x_{2}+4 x_{3}=0\cdots(iii)\\ \end{align*} Homogenous system has non-trivial solution, i... \ x_3 \end{array} \right]$ =====Question 2(ii)===== Find the value of $\lambda$ for which the s... i)}\\ &2 x_{1}+\lambda x_{2}+x_{3}=0 \quad \text{(ii)}\\ &x_{1}-2 x_{2}+\lambda x_{3}=0 \quad \text{(i
- Question 2(i, ii, iii, iv and v) Exercise 8.3 @math-11-nbf:sol:unit08
- ====== Question 2(i, ii, iii, iv and v) Exercise 8.3 ====== Solutions of Question 2(i, ii, iii, iv and v) of Exercise 8.3 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbo
- Unit 08: Fundamental of Trigonometry
- * [[math-11-nbf:sol:unit08:ex8-2-p6|Question 8(1, ii & iii) ]] * [[math-11-nbf:sol:unit08:ex8-2-p7|Question 8(iv, v & vi) ]] * [[math-11-nbf:sol:unit0... * [[math-11-nbf:sol:unit08:ex8-3-p1|Question 1(i, ii, iii & iv) ]] * [[math-11-nbf:sol:unit08:ex8-3-p2|Question 1(v, vi, vii & viii)]] * [[math-11-nbf
- Question 3, Exercise 2.6 @math-11-nbf:sol:unit02
- 9}, \quad z = -\frac{63}{19}$$ =====Question 3(ii)===== Solve the system of linear equation by Gaus... uad \cdots (i) \\ 2x + 2y + 6z &= 1 \quad \cdots (ii) \\ 3x - 4y - 5z &= 3 \quad \cdots (iii) \end{align*} The associated augmented matrix is: \begin{alig... of equations has no solution. =====Question 3(iii)===== Solve the system of linear equation by Gau
- Question 8(i, ii & iii) Exercise 8.2 @math-11-nbf:sol:unit08
- ====== Question 8(i, ii & iii) Exercise 8.2 ====== Solutions of Question 8(i, ii & iii) of Exercise 8.2 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Mat
- Question 1(i, ii, iii & iv) Exercise 8.3 @math-11-nbf:sol:unit08
- ====== Question 1(i, ii, iii & iv) Exercise 8.3 ====== Solutions of Question 1(i, ii, iii & iv) of Exercise 8.3 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of
- Question 3(i, ii, iii, iv & v) Exercise 8.3 @math-11-nbf:sol:unit08
- ====== Question 3(i, ii, iii, iv & v) Exercise 8.3 ====== Solutions of Question 3(i, ii, iii, iv & v) of Exercise 8.3 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook
- Question 2, Review Exercise @math-11-nbf:sol:unit08
- lign*} As $\theta$ is obtuse, so $\theta$ lies in II Q. This implies $\cos \theta <0$, thus $$\cos \th... phi)&=\frac{56}{65} \end{align*} =====Question 2(ii)===== Given that $\sin \theta=\dfrac{3}{5}, \sin ... lign*} As $\theta$ is obtuse, so $\theta$ lies in II Q. This implies $\cos \theta <0$, thus $$\cos \th... \ &= -\frac{56}{33} \end{align*} =====Question 2(iii)===== Given that $\sin \theta=\dfrac{3}{5}, \sin
- Question 3, Exercise 1.2 @math-11-nbf:sol:unit01
- a+i(0)=a$$ This gives $z$ is real. ====Question 3(ii)==== Prove that for $z \in \mathbb{C}$. $\dfrac{z... c{I m z}{R e z}\right)\end{align} ====Question 3(iii)==== Prove that for $z \in \mathbb{C}$. $z$ is e... e $$z^2=x^2 \quad \text{ or } \quad z^2=-y^2. ...(ii)$$ From (i) and (ii), we have $$(\overline{z})^{2}=z^{2}$$ Conversly, suppose that \begin{align}&(\ov
- Question 5 and 6, Exercise 8.1 @math-11-nbf:sol:unit08
- \beta$ in QIII, find \\ (i) $\sin(\alpha-\beta)$ (ii) $\cos(\alpha-\beta)$ (iii) $\tan(\alpha-\beta)$. ** Solution. ** Given: $\cos\alpha=-\dfrac{7}{25}... -\frac{56}{425} =-\frac{416}{425} \end{align*} (ii) $\cos(\alpha-\beta)$ \begin{align*}\cos (\alpha-... }-\frac{192}{425} =-\frac{87}{425} \end{align*} (iii) $\tan(\alpha-\beta)$ \begin{align*}\tan(\alpha-
- Question 7, Exercise 8.1 @math-11-nbf:sol:unit08
- a=\dfrac{4}{3}$ find \\ (i) $\sin(\alpha+\beta)$ (ii) $\cos(\alpha+\beta)$ (iii) $\tan(\alpha+\beta)$. ** Solution. ** Given: $\sin \alpha=\dfrac{12}{13... rac{20}{65} \\ & = \dfrac{56}{65}. \end{align*} (ii) $\cos(\alpha + \beta)$ \begin{align*} \cos(\alph... frac{48}{65} \\ & = -\dfrac{33}{65}\end{align*} (ii) $\tan(\alpha + \beta)$ \begin{align*} \tan(\alph
- Question 8, Exercise 8.1 @math-11-nbf:sol:unit08
- <\beta<2 \pi$ find: \\ (i) $\csc (\alpha+\beta)$ (ii) $\sec (\alpha+\beta)$ (iii) $\cot (\alpha+\beta)$ ** Solution. ** Given: $\sin \alpha=\dfrac{3}{5... dfrac{16}{65}} \\ &= \frac{65}{16}. \end{align*} (ii) \begin{align*} \cos (\alpha + \beta) &= \cos \a... dfrac{63}{65}} \\ &= \frac{65}{63}. \end{align*} (iii) \begin{align*} \cot (\alpha + \beta) &= \frac{
- Question 7 Exercise 8.2 @math-11-nbf:sol:unit08
- 4\alpha}{8} \end{align*} GOOD =====Question 7(ii)===== Rewrite in terms of an expression containin... \cos 4\alpha\right) \end{align*} =====Question 7(iii)===== Rewrite in terms of an expression containi... "right"><btn type="success">[[math-11-nbf:sol:unit08:ex8-2-p6|Question 8(i, ii & iii) >]]</btn></text>