Search
You can find the results of your search below.
Fulltext results:
- Question 10, Exercise 1.2
- = \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 6(i-ix), Exercise 1.4
- }} \right) \\ =& 1-i. \end{align} =====Question 6(ii)===== Write a given complex number in the algebra... }}{2} - \frac{5}{2}i \end{align*} =====Question 6(iii)===== Write a given complex number in the algebr... \frac{i}{\sqrt{2}} \end{align*} =====Question 6(vii)===== Write a given complex number in the algebra... swers, not approximate answers. =====Question 6(viii)===== Write a given complex number in the algebr
- Question 6(x-xvii), Exercise 1.4
- ====== Question 6(x-xvii), Exercise 1.4 ====== Solutions of Question 6(x-xvii) of Exercise 1.4 of Unit 01: Complex Numbers. Thi... o yourself as previous parts.// =====Question 6(xii)===== Write a given complex number in the algebra... Do yourself as previous parts.// =====Question 6(xiii)===== Write a given complex number in the algebr
- Question 2, Exercise 1.1
- +(i2+i4)\\ =&5+i6\end{align} GOOD ====Question 2(ii)==== Write the following complex number in the fo... )+(3i-5i)\\ =&2-2i\end{align} GOOD ====Question 2(iii)==== Write the following complex number in the f... }+\dfrac{9}{10}i\end{align} GOOD ====Question 2(vii)==== Write the following complex number in the fo... =&3-i^2+3i-i\\ =&4+2i\end{align} ====Question 2(viii)==== Write the following complex number in the f
- Question 3, Exercise 1.2
- 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 1, Exercise 1.3
- = &(z + 13i)(z - 13i). \end{align} ====Question 1(ii)==== Factorize the polynomial into linear functio... = &2(z + 3i)(z - 3i) \end{align} ====Question 1(iii)==== Factorize the polynomial into linear functi... \ =& (z-1)(z-2)(z+3). \end{align} ====Question 1(vii)==== Factorize the polynomial into linear functio... z + 4)(z - 5). \end{align} GOOD ====Question 1(viii)==== Factorize the polynomial into linear functi
- Question 1, Review Exercise
- 1" collapsed="true">%%(c)%%: complex</collapse> ii. Every complex number has $\operatorname{part}(\m... pse id="a2" collapsed="true">(b): two</collapse> iii. Magnitude of a complex number $z$ is the distan... $\overline{z_{1}}=-\overline{z_{2}}$</collapse> vii. Diagram representing a complex number is called ... a7" collapsed="true">%%(c)%%: argand</collapse> viii. If $\mathrm{z}=3+4 i$ then $\mathrm{z}^{-1}$ is
- Question 7, Exercise 1.4
- y = 1. \end{align*} As required. =====Question 7(ii)===== Convert the following equations and inequat... lies & x^2+y^2 = 4. \end{align*} =====Question 7(iii)===== Convert the following equations and inequa... [math-11-nbf:sol:unit01:ex1-4-p7|< Question 6(x-xvii)]]</btn></text> <text align="right"><btn type="su
- Question 1, Exercise 1.1
- ot(-1)\\ &=-i.\end{align} GOOD ====Question 1(ii)==== Evaulate ${{\left( -i \right)}^{6}}$. **Sol... -(-1)\cdot i = i. \end{align} GOOD ====Question 1(iii)==== Evaluate ${{\left( -1 \right)}^{\frac{-13}{
- Question 3, Exercise 1.1
- }{2}-\dfrac{9}{2}i\end{align} GOOD ====Question 3(ii)==== Simplify the following $\dfrac{1+i}{(2+i)^2}... -\dfrac{1}{25}i. \end{align} GOOD ====Question 3(iii)==== Simplify the following $\dfrac{1}{3+i}-\dfr
- Question 4, Exercise 1.1
- . Hence $x=-2$ and $y=2$. GOOD ====Question 4(ii)==== Find the values of real number $x$ and $y$ ... 4}{3}$ and $y=\dfrac{5}{3}$. GOOD ====Question 4(iii)==== Find the values of real number $x$ and $y$
- Question 6, Exercise 1.1
- $z=4-3 i$, then $\bar{z}=4+3i$. ====Question 6(ii)==== Find the conjugate of the complex number $3 ... +8$. **Solution.** Do Yourself ====Question 6(iii)==== Find the conjugate of the complex number $2
- Question 7, Exercise 1.1
- ce $|11+12 i|=\sqrt{265}$. GOOD ====Question 7(ii)==== Find the magnitude of the $(2+3 i)-(2+6 i)$.... nce $$|(2+3 i)-(2+6 i)|=3.$$ GOOD ====Question 7(iii)==== Find the magnitude of the $(2-i)(6+3 i)$.
- Question 2, Exercise 1.2
- oved $$(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 8, Exercise 1.2
- 5=0, \end{align} as required. GOOD ====Question 8(ii)==== Write $|z-1|=|\bar{z}+i|$ in terms of $x$ an... =0, \end{align} as required. GOOD ====Question 8(iii)==== Write $|z-4 i|+|z+4 i|=10$ in terms of $x$