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Question 2, Exercise 1.1
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abad, Pakistan. ====Question 2(i)==== Write the following complex number in the form $x+iy$: $(3+2i)+(2+4i)... end{align} GOOD ====Question 2(ii)==== Write the following complex number in the form $x+iy$: $(4+3i)-(2+5i)... end{align} GOOD ====Question 2(iii)==== Write the following complex number in the form $x+iy$: $(4+7i)+(4-7i)... end{align} GOOD ====Question 2(iv)==== Write the following complex number in the form $x+iy$: $(2+5i)-(2-5i)
Question 7, Exercise 1.4
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, Pakistan. =====Question 7(i)===== Convert the following equation in Cartesian form: $\arg (z-1)=-\dfrac{\... s required. =====Question 7(ii)===== Convert the following equations and inequations in Cartesian form: $z \... end{align*} =====Question 7(iii)===== Convert the following equations and inequations in Cartesian form: $-\... As required. =====Question 7(iv)===== Convert the following equations and inequations in Cartesian form: $0 \
Question 3, Exercise 1.1
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ad, Pakistan. ====Question 3(i)==== Simplify the following $\dfrac{(2+i)(3-2i)}{1+i}$ **Solution.** \begin{... d{align} GOOD ====Question 3(ii)==== Simplify the following $\dfrac{1+i}{(2+i)^2}$ **Solution.** \begin{ali... align} GOOD ====Question 3(iii)==== Simplify the following $\dfrac{1}{3+i}-\dfrac{1}{3-i}$ **Solution.** \... d{align} GOOD ====Question 3(iv)==== Simplify the following $(1+i)^{-2}+(1-i)^{-2}$ **Solution.** \begin{al
Question 4, Exercise 1.1
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values of real number $x$ and $y$ in each of the following: $(2+3i)x+(1+3i)y+2=0$ **Solution.** \begin{al... values of real number $x$ and $y$ in each of the following: $\dfrac{x}{(1+i)}+\dfrac{y}{1-2i}=1$ **Solution... values of real number $x$ and $y$ in each of the following: $\dfrac{x}{(2+i)}=\dfrac{1-5i}{(3-2i)}+\dfrac{y}... values of real number $x$ and $y$ in each of the following: $x(1+i)^2+y(2-i)^2=3+10i$ **Solution.** \begi
Question 9, Exercise 1.2
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Suppose $z=3 - \sqrt{-4}=3-2i$. We will use the following formulas: \[\text{Re}(z^{-2}) = \frac{(\text{Re}... i}{3-i}\right)^{-1}$. **Solution.** We use the following formulas: \[Re\left(\left(\frac{x_1 + i y_1}{x_... i}\right)^{-2}$. **Solution.** We will use the following formulas: \begin{align} &Re\left(\left(\frac{x_... i}\right)^{2}$. **Solution.** We will use the following formulas: \[\text{Re}\left(\left(\frac{x_1 + i
Question 2, Review Exercise
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===== Question 2(i) ===== Find the value of the following: $i^{2}+i^{4}+i^{6}+\cdots+i^{100}$\\ ** Solutio... ===== Question 2(ii) ===== Find the value of the following: $\left|\dfrac{(3-2 i)(1+i)}{2-3 i}\right|$ ** S... ==== Question 2(iii) ===== Find the value of the following: $|\overline{(3-2 i)(4-i)}|$ ** Solution. ** \b... ===== Question 2(iv) ===== Find the value of the following: $\left(\dfrac{3+5 i}{2-3 i}\right)^{-1}$ ** So
Question 1, Exercise 1.4
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ght). \] GOOD =====Question 1(ii)===== Write the following complex number $3-i \sqrt{3}$ in polar form. ** ... \end{align} =====Question 1(iii)===== Write the following complex number $-2-i 2$ in polar form. ** Soluti... nd{align} GOOD =====Question 1(iv)===== Write the following complex number $\dfrac{i-1}{\cos \dfrac{\pi}{3}+i
Question 10, Exercise 1.4
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uestion 10(i)===== Find the impedance $Z$ for the following values: $E=(-50+100 i)$ volts, $I=(-6-2 i)$ amps.... estion 10(ii)===== Find the impedance $Z$ for the following values: $E=(100+10 i)$ volts, $I=(-8+3 i) \mathrm
Question 3, Review Exercise
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kistan. ===== Question 3(i) ===== Factorize the following: $3 x^{2}+108$ ** Solution. ** \begin{align*} &... {align*} ===== Question 3(ii) ===== Factorize the following: $4 x^{2}+40$ ** Solution. ** \begin{align*} &4