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 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}$$ Conversly, suppose that \begin{align}&(\ov
- Question 1, Exercise 1.1
- ot(-1)\\ &=-i.\end{align} GOOD ====Question 1(ii)==== Evaulate ${{\left( -i \right)}^{6}}$. **Sol... -(-1)\cdot i = i. \end{align} GOOD ====Question 1(iii)==== Evaluate ${{\left( -1 \right)}^{\frac{-13}{
- Question 2, Exercise 1.1
- +(i2+i4)\\ =&5+i6\end{align} GOOD ====Question 2(ii)==== Write the following complex number in the fo... )+(3i-5i)\\ =&2-2i\end{align} GOOD ====Question 2(iii)==== Write the following complex number in the f
- Question 3, Exercise 1.1
- }{2}-\dfrac{9}{2}i\end{align} GOOD ====Question 3(ii)==== Simplify the following $\dfrac{1+i}{(2+i)^2}... -\dfrac{1}{25}i. \end{align} GOOD ====Question 3(iii)==== Simplify the following $\dfrac{1}{3+i}-\dfr
- Question 4, Exercise 1.1
- . Hence $x=-2$ and $y=2$. GOOD ====Question 4(ii)==== Find the values of real number $x$ and $y$ ... 4}{3}$ and $y=\dfrac{5}{3}$. GOOD ====Question 4(iii)==== Find the values of real number $x$ and $y$
- Question 6, Exercise 1.1
- $z=4-3 i$, then $\bar{z}=4+3i$. ====Question 6(ii)==== Find the conjugate of the complex number $3 ... +8$. **Solution.** Do Yourself ====Question 6(iii)==== Find the conjugate of the complex number $2
- Question 7, Exercise 1.1
- ce $|11+12 i|=\sqrt{265}$. GOOD ====Question 7(ii)==== Find the magnitude of the $(2+3 i)-(2+6 i)$.... nce $$|(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 $x$
- Question 9, Exercise 1.2
- &= \dfrac{1}{5}. \end{align} GOOD ====Question 9(ii)==== Find real and imaginary parts of $(3-\sqrt{... part is \(\dfrac{12}{169}\). GOOD ====Question 9(iii)==== Find real and imaginary parts of $\left(\d
- Question 1, Exercise 1.3
- = &(z + 13i)(z - 13i). \end{align} ====Question 1(ii)==== Factorize the polynomial into linear functio... = &2(z + 3i)(z - 3i) \end{align} ====Question 1(iii)==== Factorize the polynomial into linear functi
- Question 2, Exercise 1.3
- utioin set=$\{3 \pm \sqrt{7}\}$. ====Question 2(ii)==== Solve the equation by completing square: $-\... ution set$=\{-5 \pm \sqrt{29}\}$ ====Question 2(iii)==== Solve the equation by completing square: $4
- Question 3, Exercise 1.3
- n set $=\{ -3 \pm \sqrt{57} \}$. ====Question 3(ii)==== Solve the quadratic equation: $z^{2}-\frac{1... c{1 \pm \sqrt{271}i}{4}\right\} $ ====Question 3(iii)==== Solve the quadratic equation: $z^{2}-6 z+25
- Question 4, Exercise 1.3
- c{2}{53}-\dfrac{7}{53}i.$$ GOOD =====Question 4(ii)===== Solve the simultaneous system of linear equ... 205} + \dfrac{177}{205}i.$$ GOOD =====Question 4(iii)===== Solve the simultaneous system of linear eq