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- Question 1, Exercise 1.1
- 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
- +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
- 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
- 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
- -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
- 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 4, Exercise 1.3
- 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 1.4
- \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
- Question 4, Exercise 1.1
- n $(3)$, we have $x=-2$. Hence $x=-2$ and $y=2$. GOOD ====Question 4(ii)==== Find the values of r... ign} Hence $x=\dfrac{4}{3}$ and $y=\dfrac{5}{3}$. GOOD ====Question 4(iii)==== Find the values of re... 3y+(2x-4y)i=3+10i\end{align} Now do yourself ====Go to ==== <text align="left"><btn type="primary">[
- Question 9, Exercise 1.2
- = -\dfrac{4}{20}\\ &= \dfrac{1}{5}. \end{align} GOOD ====Question 9(ii)==== Find real and imaginary ... \) and the imaginary part is \(\dfrac{12}{169}\). GOOD ====Question 9(iii)==== Find real and imaginary... is \(-1\) and the imaginary part is \(-1\). ====Go to ==== <text align="left"><btn type="primary">[[
- Question 1, Exercise 1.3
- -5(z + 4))\\ &=(z + 3)(z + 4)(z - 5). \end{align} GOOD ====Question 1(viii)==== Factorize the polyno... + 5)) \\ =&(z - 2) (z + 5) (2z + 3). \end{align} GOOD ====Question 1(ix)==== Factorize the polynomia... )+1(4z-1)\\ = &(4z - 11)(z + 1). \end{align} ====Go to ==== <text align="left"><btn type="success">[[
- Question 5, Exercise 1.1
- . }\,y=-1.\end{align} Thus we have $z=x+iy=4-i$. GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit01:ex1-1-p4|< Question
- Question 6, Exercise 1.1
- },$ then $\bar{z}=-\dfrac{5 }{2}i-\dfrac{7}{8}$. GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit01:ex1-1-p5|< Questio
- Question 4, Exercise 1.2
- ow \quad & |z_2|=\dfrac{16}{\sqrt{13}}\end{align} GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit01:ex1-2-p3|< Question
- Question 2, Exercise 1.4
- rac{1}{2}i \end{align} Which is rectangular form. GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit01:ex1-4-p1|< Question