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- Question 1, Exercise 1.1 @math-11-nbf:sol:unit01
- because i^2=-1\\ &=i\cdot(-1)\\ &=-i.\end{align} GOOD ====Question 1(ii)==== Evaulate ${{\left( -i... )^{11} \cdot i \\ &=-(-1)\cdot i = i. \end{align} GOOD ====Question 1(iii)==== Evaluate ${{\left( -1 \... =\dfrac{i}{-\left( -1 \right)}\\ &=i\end{align} GOOD ====Question 1(iv)==== Evaluate $\dfrac{2}{(-1)^{\frac{3}{2}}}$. GOOD **Solution.** \begin{align}{{\left( -1 \right
- Question 2, Exercise 1.1 @math-11-nbf:sol:unit01
- +i2)+(2+i4)\\ =&(3+2)+(i2+i4)\\ =&5+i6\end{align} GOOD ====Question 2(ii)==== Write the following com... +3i)-(2+5i)\\ =&(4-2)+(3i-5i)\\ =&2-2i\end{align} GOOD ====Question 2(iii)==== Write the following com... i)+(4-7i)\\ =&(4+4)+(7i-7i)\\ =&8+0i. \end{align} GOOD ====Question 2(iv)==== Write the following com... )-(2-5i)\\ =&(2-2)+(5i+5i)\\ =&0+10i. \end{align} GOOD ====Question 2(v)==== Write the following comp
- Question 8, Exercise 1.2 @math-11-nbf:sol:unit01
- ies & 4x^2+4y^2-4y-15=0, \end{align} as required. GOOD ====Question 8(ii)==== Write $|z-1|=|\bar{z}+i|... \\ \implies & x - y =0, \end{align} as required. GOOD ====Question 8(iii)==== Write $|z-4 i|+|z+4 i|=... s & 25x^2 + 9y^2 = 225, \end{align} as required. GOOD ====Question 8(iv)==== Write $\frac{1}{2} \oper... } y=4 \\ \implies & y=8, \end{align} as required. GOOD ====Question 8(v)==== Write $lm\left(\dfrac{z-1
- Question 10, Exercise 1.2 @math-11-nbf:sol:unit01
- overline{z_1} \right| = \sqrt{13}.$$ As required. GOOD ====Question 10(ii)==== For $z_{1}=-3+2 i$ and ... ght)} = \frac{\overline{z_1}}{\overline{z_2}}. \] GOOD ====Question 10(iii)==== For $z_{1}=-3+2 i$ an... = \overline{z_1} \overline{z_2}, \] as required. GOOD ====Question 10(iv)==== For $z_{1}=-3+2 i$ and... e{z_1 + z_2} = \overline{z_1} + \overline{z_2}.\] GOOD ====Question 10(v)==== For $z_{1}=-3+2 i$ and $
- Question 3, Exercise 1.1 @math-11-nbf:sol:unit01
- -9i}{2}\\ =&\dfrac{7}{2}-\dfrac{9}{2}i\end{align} GOOD ====Question 3(ii)==== Simplify the following $... 25}\\ =&\dfrac{7}{25}-\dfrac{1}{25}i. \end{align} GOOD ====Question 3(iii)==== Simplify the following... \ =&-\dfrac{2}{10}i\\ =&-\dfrac{1}{5}i\end{align} GOOD ====Question 3(iv)==== Simplify the following $... \\ =&\dfrac{1}{2i}-\dfrac{1}{2i}\\ =&0\end{align} GOOD ====Question 3(v)==== Simplify: $(2+i)^2+\dfra
- Question 7, Exercise 1.1 @math-11-nbf:sol:unit01
- rt{265}\end{align} Hence $|11+12 i|=\sqrt{265}$. GOOD ====Question 7(ii)==== Find the magnitude of ... = 3. \end{align} Hence $$|(2+3 i)-(2+6 i)|=3.$$ GOOD ====Question 7(iii)==== Find the magnitude of t... t{5} = 15.\end{align} Hence $|(2-i)(6+3 i)|=15$. GOOD ====Question 7(iv)==== Find the magnitude of th... dfrac{3-2 i}{2+i} \right|=\sqrt{\dfrac{13}{5}}$. GOOD ====Question 7(v)==== Find the magnitude of the
- Question 3(vi, vii, viii, ix & x) Exercise 8.3 @math-11-nbf:sol:unit08
- = \sec y(\sin 4y - \sin 2y)\\ &= RHS \end{align*} GOOD =====Questio 3(vii)===== Prove the identity $\d... & = \tan 5\beta \cot \beta\\ &= RHS \end{align*} GOOD =====Questio 3(viii)===== Prove the identity $\... ta} \\ & = -2 \cos 2\theta \\ &= RHS \end{align*} GOOD :!: **Correction:**\\ The corrected version of... \ & = \cos 7x \sec 5x \cot x\\ &=RHS \end{align*} GOOD =====Questio 3(x)===== Prove the identity $\df
- Question 1, Exercise 9.1 @math-11-nbf:sol:unit09
- m value $(M) = 4$ \\ and minimum value $(m) = 0$. GOOD **Alternative Method:** Given: $$y=2-2 \opera... ximum value (M) = 4 \\ and mimimum value (m) = 0. GOOD =====Question 1(ii)===== Find the maximum an... 7}{6}$ \\ and minimum value $(m) = \dfrac{1}{6}$. GOOD **Alternative Method:** Given: $$y=\dfrac{2}{... 7}{6}$ \\ and mimimum value $(m) = \dfrac{1}{6}$. GOOD =====Question 1(iii)===== Find the maximum and
- Question 4, Exercise 1.3 @math-11-nbf:sol:unit01
- 45}{106}i, \omega=\dfrac{2}{53}-\dfrac{7}{53}i.$$ GOOD =====Question 4(ii)===== Solve the simultaneo... \omega = \dfrac{199}{205} + \dfrac{177}{205}i.$$ GOOD =====Question 4(iii)===== Solve the simultaneo... 9}i;\omega= -\dfrac{288}{109}+ \dfrac{88}{109}i$$ GOOD =====Question 4(iv)===== Solve the simultaneou... 1}{53}i; \omega=\dfrac{68}{53}-\dfrac{80}{53}i.$$ GOOD ====Go to ==== <text align="left"><btn type="p
- Question 1, Exercise 4.2 @math-11-nbf:sol:unit04
- ign*} Hence $a_1=4$, $a_2=7$, $a_3=10$, $a_4=13$. GOOD =====Question 1(ii)===== Find the first four t... gn*} Hence $a_1=7$, $a_2=12$, $a_3=17$, $a_4=22$. GOOD =====Question 1(iii)===== Find the first four... n*} Hence $a_1=16$, $a_2=14$, $a_3=12$, $a_4=10$. GOOD =====Question 1(iv)===== Find the first four ... n*} Hence $a_1=38$, $a_2=34$, $a_3=30$, $a_4=26$. GOOD =====Question 1(v)===== Find the first four
- Question 13, Exercise 4.2 @math-11-nbf:sol:unit04
- frac{24}{2} = 12. \end{align*} Hence A.M. = $12$. GOOD =====Question 13(ii)===== Find A.M. between $3... = \frac{10}{2}= 5. \end{align*} Hence A.M. = $5$. GOOD =====Question 13(iii)===== Find A.M. between $... \sqrt{5} \end{align*} Hence A.M. = $ 4 \sqrt{5}$. GOOD =====Question 13(iv)===== Find A.M. between $2... 4 \end{align*} Hence A.M. = $\dfrac{7y}{2} + 4$. GOOD ====Go to ==== <text align="left"><btn type="
- Question 2, Exercise 8.1 @math-11-nbf:sol:unit08
- \ & = \dfrac{\sqrt{3}+1}{2\sqrt{2}}. \end{align*} GOOD ===== Question 2(b)===== Use the value of... & = -\dfrac{\sqrt{3}+1}{2\sqrt{2}}. \end{align*} GOOD **Alternative Method (if $\cos 15^{\circ}$ is ... & = -\dfrac{\sqrt{3}+1}{2\sqrt{2}}. \end{align*} GOOD ===== Question 2(c)===== Use the value of $\co... rc = \frac{\sqrt{3}+1}{\sqrt{3}-1}} \end{align*} GOOD ====Go to ==== <text align="left"><btn type="p
- Question 8(xix, xx, xxi & xxii) Exercise 8.2 @math-11-nbf:sol:unit08
- cos\alpha}\\ & = \sec\alpha \\ &=RHS \end{align*} GOOD =====Question 8(xx)===== Verify the identi... \frac{\beta}{2} \\ & = 1 \\ & = RHS \end{align*} GOOD =====Question 8(xxi)===== Verify the identi... } \\ & = 2\cos y \sec 2y \\ & = LHS \end{align*} GOOD =====Question 8(xxii)===== Verify the identit... } \\ & = 2\sin y \sec 2y \\ & = LHS \end{align*} GOOD ====Go to ==== <text align="left"><
- Question 1(v, vi, vii & viii) Exercise 8.3 @math-11-nbf:sol:unit08
- =& \frac{1}{2}[\cos(6u) - \cos(4u) ] \end{align*} GOOD =====Question 1(vi)===== Use the product-to-sum... = \cos 80^{\circ} - \cos 120^{\circ} \end{align*} GOOD :!: =====Question 1(vii)===== Use the product-t... [ \sin 40^{\circ} - \sin 6^{\circ} ] \end{align*} GOOD =====Question 1(viii)===== Use the product-to-... & \sin 104^{\circ} - \sin 8^{\circ} \end{align*} GOOD ====Go to ==== <text align="left"><btn type
- Question 1, Exercise 1.4 @math-11-nbf:sol:unit01
- \frac{\pi}{3} + i \sin \frac{\pi}{3} \right). \] GOOD =====Question 1(ii)===== Write the following c... }{4} + i \sin \frac{5\pi}{4} \right). \end{align} GOOD =====Question 1(iv)===== Write the following co... {12}+ i \sin \frac{5\pi}{12} \right). \end{align} GOOD ====Go to ==== <text align="left"><btn type="success">[[math-11-nbf:sol:unit01:ex1-4-p2|Que