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- Question 6(x-xvii), Exercise 1.4
- Question 8(i, ii & iii) Exercise 8.2
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- Question 1(i, ii, iii & iv) Exercise 8.3
- Question 1(v, vi, vii & viii) Exercise 8.3
- Question 2(i, ii, iii, iv and v) Exercise 8.3
- Question 3(i, ii, iii, iv & v) Exercise 8.3
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- Question 3(xi, xii & xiii) Exercise 8.3
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Fulltext results:
- 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}}{\o... overline{z_1}\,\, \overline{z_2} & = 3 - 11i. -- (ii) \end{align} From (i) and (ii), we have \[ \ov
- 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{al... m has non-trivial solution. \text{By}\quad(i)-2(ii), we have \begin{align*} &\begin{array}{cccc} 2x_... d{array} \right] \end{align*} =====Question 1(ii)===== Solve the system of homogeneous linear equa... ad \text{(i)}\\ &x_1 + x_2 + x_3 = 0 \quad \text{(ii)}\\ &x_1 - 4x_2 + 3x_3 = 0 \quad \text{(iii)} \en
- 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{a... \ 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... (i)} \\ 2x_{1} + 2x_{2} + x_{3} &= 0 \quad \text{(ii)} \\ x_{1} - 2x_{2} + 2x_{3} &= 0 \quad \text{(ii
- 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: Funda... cos 20^\circ \end{align*} GOOD =====Question 2(ii)===== Rewrite the sum or difference as a product ... ><btn type="success">[[math-11-nbf:sol:unit08:ex8-3-p5|Question 3(i, ii, iii, iv & v) >]]</btn></text>
- 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... lign*} As $\theta$ is obtuse, so $\theta$ lies in II Q. This implies $\cos \theta <0$, thus $$\cos \th
- Unit 08: Fundamental of Trigonometry @math-11-nbf:sol
- * [[math-11-nbf:sol:unit08:ex8-2-p6|Question 8(1, ii & iii) ]] * [[math-11-nbf:sol:unit08:ex8-2-p7|Q... * [[math-11-nbf:sol:unit08:ex8-3-p1|Question 1(i, ii, iii & iv) ]] * [[math-11-nbf:sol:unit08:ex8-3-... * [[math-11-nbf:sol:unit08:ex8-3-p5|Question 3(i, ii, iii, iv & v)]] * [[math-11-nbf:sol:unit08:ex8-
- Question 3, Exercise 1.2 @math-11-nbf:sol:unit01
- a+i(0)=a$$ This gives $z$ is real. ====Question 3(ii)==== Prove that for $z \in \mathbb{C}$. $\dfrac{z... 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 3, Exercise 2.6 @math-11-nbf:sol:unit02
- 9}, \quad z = -\frac{63}{19}$$ =====Question 3(ii)===== Solve the system of linear equation by Gaus... uad \cdots (i) \\ 2x + 2y + 6z &= 1 \quad \cdots (ii) \\ 3x - 4y - 5z &= 3 \quad \cdots (iii) \end{ali... = 2 \quad \cdots (i) \\ 2y - z &= 3 \quad \cdots (ii) \\ x + 3y &= 5 \quad \cdots (iii) \end{align*} T
- Question 7, Exercise 8.1 @math-11-nbf:sol:unit08
- a=\dfrac{4}{3}$ find \\ (i) $\sin(\alpha+\beta)$ (ii) $\cos(\alpha+\beta)$ (iii) $\tan(\alpha+\beta)$.... rac{20}{65} \\ & = \dfrac{56}{65}. \end{align*} (ii) $\cos(\alpha + \beta)$ \begin{align*} \cos(\alph... frac{48}{65} \\ & = -\dfrac{33}{65}\end{align*} (ii) $\tan(\alpha + \beta)$ \begin{align*} \tan(\alph
- Question 8(i, ii & iii) Exercise 8.2 @math-11-nbf:sol:unit08
- ====== Question 8(i, ii & iii) Exercise 8.2 ====== Solutions of Question 8(i, ii & iii) of Exercise 8.2 of Unit 08: Fundamental of... a) \\ &=RHS \end{align*} GOOD =====Question 8(ii)===== Verify the identities: $\tan 2 x=\dfrac{1}{
- Question 1(i, ii, iii & iv) Exercise 8.3 @math-11-nbf:sol:unit08
- ====== Question 1(i, ii, iii & iv) Exercise 8.3 ====== Solutions of Question 1(i, ii, iii & iv) of Exercise 8.3 of Unit 08: Fundamenta... (26x)+\sin(6x)] \end{align*} GOOD =====Question 1(ii)===== Use the product-to-sum formula to change th
- Question 3(i, ii, iii, iv & v) Exercise 8.3 @math-11-nbf:sol:unit08
- ====== Question 3(i, ii, iii, iv & v) Exercise 8.3 ====== Solutions of Question 3(i, ii, iii, iv & v) of Exercise 8.3 of Unit 08: Fundame... )} \\ & = LHS \end{align*} GOOD =====Questio 3(ii)===== Prove the identity $\dfrac{6 \cos 8u \sin 2
- Question 2, Exercise 9.1 @math-11-nbf:sol:unit09
- value $(m) = \dfrac{1}{7}$. GOOD =====Question 2(ii)===== Find the maximum and minimum values of the ... {{ :math-11-nbf:sol:unit09:math-11-nbf-ex9-1-q2_ii_.png?400 |Graph of y}} **From the graph, we see ... theta-5)}$ ** Solution. ** **Same as Question 2(ii), we see that given $\dfrac{1}{\frac{1}{3}-4 \sin
- Question 2, Exercise 1.2 @math-11-nbf:sol:unit01
- oved $$(z_1 z_3) (z_2 z_4)=z_3 (z_1 z_2) z_4 ... (ii)$$ From (i) and (ii), we have the required result. **Remark:** For any three complex numbers $z_1$,
- Question 13, Exercise 2.2 @math-11-nbf:sol:unit02
- ix} 4 & 3 & 2 \\ 1 & -3 & 0 \end{pmatrix} \cdots (ii) \end{align*} From (i) we have \begin{align*} Y =... 7 \end{pmatrix} \end{align*} Put value of $Y$ in (ii), we have \begin{align*} X + 3\left(2X - \begin{