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- Question 9, Exercise 1.2
- oard, Islamabad, Pakistan. ====Question 9(i)==== Find real and imaginary parts of $(2+4 i)^{-1}$. **So... ac{1}{5}. \end{align} GOOD ====Question 9(ii)==== Find real and imaginary parts of $(3-\sqrt{-4})^{-2}$... \(\dfrac{12}{169}\). GOOD ====Question 9(iii)==== Find real and imaginary parts of $\left(\dfrac{7+2 i}... t is \(\dfrac{-13}{53}\). ====Question 9(iv)==== Find real and imaginary parts of $\left(\dfrac{4+2 i}
- Question 7, Exercise 1.1
- oard, Islamabad, Pakistan. ====Question 7(i)==== Find the magnitude of the $11+12 i$. **Solution.** ... 12 i|=\sqrt{265}$. GOOD ====Question 7(ii)==== Find the magnitude of the $(2+3 i)-(2+6 i)$. **Soluti... +3 i)-(2+6 i)|=3.$$ GOOD ====Question 7(iii)==== Find the magnitude of the $(2-i)(6+3 i)$. **Solution.... $|(2-i)(6+3 i)|=15$. GOOD ====Question 7(iv)==== Find the magnitude of the $\dfrac{3-2 i}{2+i}$. **Sol
- Question 4, Exercise 1.1
- ard, Islamabad, Pakistan. ====Question 4(i)==== Find the values of real number $x$ and $y$ in each of ... $x=-2$ and $y=2$. GOOD ====Question 4(ii)==== Find the values of real number $x$ and $y$ in each of ... $y=\dfrac{5}{3}$. GOOD ====Question 4(iii)==== Find the values of real number $x$ and $y$ in each of ... d{align} Now do yourself. ====Question 4(iv)==== Find the values of real number $x$ and $y$ in each of
- Question 6, Exercise 1.1
- oard, Islamabad, Pakistan. ====Question 6(i)==== Find the conjugate of the complex number $4-3 i$. **S... i$, then $\bar{z}=4+3i$. ====Question 6(ii)==== Find the conjugate of the complex number $3 i+8$. **S... olution.** Do Yourself ====Question 6(iii)==== Find the conjugate of the complex number $2+\sqrt{\dfr... =2-\sqrt{\dfrac{1}{5}}i$$ ====Question 6(iv)==== Find the conjugate of the complex number $\dfrac{5 }{2
- Question 2, Review Exercise
- Islamabad, Pakistan. ===== Question 2(i) ===== Find the value of the following: $i^{2}+i^{4}+i^{6}+\c... =& 0. \end{align*} ===== Question 2(ii) ===== Find the value of the following: $\left|\dfrac{(3-2 i)... \sqrt{2}\end{align} ===== Question 2(iii) ===== Find the value of the following: $|\overline{(3-2 i)(4... qrt{221}. \end{align*} ===== Question 2(iv) ===== Find the value of the following: $\left(\dfrac{3+5 i}{
- Question 10, Exercise 1.4
- , Islamabad, Pakistan. =====Question 10(i)===== Find the impedance $Z$ for the following values: $E=(-... impedance $Z=25-175i$. =====Question 10(ii)===== Find the impedance $Z$ for the following values: $E=(1
- Question 5, Review Exercise
- rd, Islamabad, Pakistan. ===== Question 5 ===== Find $z$ when $(z-3 i)(2+5 i)=3-4 i$. ** Solution. ** ===== Question 5 ===== Find $z$ when $(z-3 i)(2+5 i)=3-4 i$. ** Solution. **
- Question 5, Exercise 1.1
- k Board, Islamabad, Pakistan. ====Question 5==== Find the complex number $z$ if $4z-3\bar{z}=\dfrac{1-1
- Question 4, Exercise 1.2
- f $z_{1}=2-3 i$ and $\left|z_{1} z_{2}\right|=16$ find $\left|z_{2}\right|$. **Solution.** Given $$z_
- Question 6, Exercise 1.2
- k Board, Islamabad, Pakistan. ====Question 6==== Find the value of $\lambda$; if $\left|\dfrac{z_{1}}{z
- Question 4, Exercise 1.3
- substituting $\omega$ back into equation $(1)$ to find $z$: \begin{align} &2iz + (3-2i)\left( \dfrac{199
- Question 9, Exercise 1.4
- t. Calculate the angle at time $\mathrm{t}=0$ and find the position of the particle. ** Solution. ** H
- Question 8, Review Exercise
- qrt{2}, \quad \theta=\dfrac{\pi}{4}.$$ We have to find $x_{\max}$. By using the formula \begin{align} &x