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- Question 1, Exercise 1.4
- kistan. =====Question 1(i)===== Write a complex number $2+i 2 \sqrt{3}$ in polar form. ** Solution. ** ... ) = \frac{\pi}{3}. \end{align} Since the complex number \( 2 + i 2 \sqrt{3} \) lies in the first quadrant... ==Question 1(ii)===== Write the following complex number $3-i \sqrt{3}$ in polar form. ** Solution. ** L... &= \frac{\pi}{6}. \end{align} Since the complex number \( 3 - i \sqrt{3} \) lies in the fourth quadrant,
- Question 6(i-ix), Exercise 1.4
- =====Question 6(i)===== Write a given complex number in the algebraic form: $\sqrt{2}\left(\cos 315^{\... n} =====Question 6(ii)===== Write a given complex number in the algebraic form: $5\left(\cos 210^{\circ}+i... } =====Question 6(iii)===== Write a given complex number in the algebraic form: $2\left(\cos \dfrac{3 \pi}... *} =====Question 6(iv)===== Write a given complex number in the algebraic form: $4\left(\cos \dfrac{5 \pi}
- Question 2, Exercise 1.1
- ====Question 2(i)==== Write the following complex number in the form $x+iy$: $(3+2i)+(2+4i)$ ** Solution.... ===Question 2(ii)==== Write the following complex number in the form $x+iy$: $(4+3i)-(2+5i)$ **Solution.*... ==Question 2(iii)==== Write the following complex number in the form $x+iy$: $(4+7i)+(4-7i)$ **Solution.*... ===Question 2(iv)==== Write the following complex number in the form $x+iy$: $(2+5i)-(2-5i)$ **Solution.*
- Question 6(x-xvii), Exercise 1.4
- . =====Question 6(x)===== Write a given complex number in the algebraic form: $7 \sqrt{2}\left(\cos \dfr... // =====Question 6(xi)===== Write a given complex number in the algebraic form: $10 \sqrt{2}\left(\cos \df... =====Question 6(xii)===== Write a given complex number in the algebraic form: $2\left(\cos\dfrac{5\pi}{2... =====Question 6(xiii)===== Write a given complex number in the algebraic form: $\dfrac{1}{\sqrt{2}}\left(
- Question 1, Review Exercise
- === Chose the correct option. i. Every real number is also a number. * (a) natural * (b) integer * %%(c)%% complex * (d) rational \\ <btn... ">%%(c)%%: complex</collapse> ii. Every complex number has $\operatorname{part}(\mathrm{s})$. * (a... >(b): two</collapse> iii. Magnitude of a complex number $z$ is the distance of $z$ from * (a) $(0,0
- Question 4, Exercise 1.1
- . ====Question 4(i)==== Find the values of real number $x$ and $y$ in each of the following: $(2+3i)x+(1... ====Question 4(ii)==== Find the values of real number $x$ and $y$ in each of the following: $\dfrac{x}{... ====Question 4(iii)==== Find the values of real number $x$ and $y$ in each of the following: $\dfrac{x}{... . ====Question 4(iv)==== Find the values of real number $x$ and $y$ in each of the following: $x(1+i)^2+y
- Question 6, Exercise 1.1
- estion 6(i)==== Find the conjugate of the complex number $4-3 i$. **Solution.** Given: $z=4-3 i$, then $... stion 6(ii)==== Find the conjugate of the complex number $3 i+8$. **Solution.** Do Yourself ====Question 6(iii)==== Find the conjugate of the complex number $2+\sqrt{\dfrac{-1}{5}}$. **Solution.** Given:... stion 6(iv)==== Find the conjugate of the complex number $\dfrac{5 }{2}i-\dfrac{7}{8}$. **Solution.** G
- Question 1, Exercise 1.2
- ====Question 1(i)==== Show that for any complex number, $\operatorname{Re}(i z)=-\operatorname{Im}(z)$. ... ====Question 1(ii)==== Show that for any complex number, $\operatorname{Im}(i z)=\operatorname{Re}(z)$.
- Question 2, Exercise 1.4
- stan. =====Question 2(i)===== Write the complex number $\left(\cos \dfrac{\pi}{6}+i \sin \dfrac{\pi}{6}\... form. =====Question 2(ii)===== Write the complex number $\dfrac{\cos \dfrac{\pi}{6} - i \sin \dfrac{\pi}{
- Question 5, Exercise 1.1
- d, Pakistan. ====Question 5==== Find the complex number $z$ if $4z-3\bar{z}=\dfrac{1-18i}{2-i}$ **Soluti
- Question 2, Exercise 1.2
- $$ Logically, z_1 z_2 z_3 has no meaning as three number cannot be multiplies simultanously, but associate
- Question 4, Review Exercise
- stan. ===== Question 4 ===== Locate the complex number $z=x+i y$ on the complex plane if $\left|\dfrac{z