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- Exercise 1.4 (Solutions)
- given on this page. This exercise consists of the question related to polar form of the complex numbers. **Question 1.** Write the following complex number in polar ... }}$\\ [[math-11-nbf:sol:unit01:ex1-4-p1|Solution: Question 1]] **Question 2.** Write the following complex number in rectangular form.\\ (i) $\left(\cos \dfrac{\pi}{
- Exercise 1.2 (Solutions)
- given on this page. This exercise consists of the question related to real and imaginary part of complex num... modulus and conjugate of the complex numbers. **Question 1.** Show that for any complex number :\\ (i) $\o... z)$\\ [[math-11-nbf:sol:unit01:ex1-2-p1|Solution: Question 1]] **Question 2.** Use the algebraic properties of complex numbers to prove that $$\left(z_{1} z_{2}\righ
- Review Exercise 1 (Solutions)
- given on this page. This exercise consists of the question related to polar form of the complex numbers. **Question 1.** Choose the correct option.\\ [[math-11-nbf:sol:unit01:re-ex-p1|Solution: Question 1]] **Question 2.** Find the value of the following:\\ (i) $i^{2}+i^{4}+i^{6}+\cdots+i^{100}$\\ (ii) $\l
- Exercise 1.1 (Solutions)
- given on this page. This exercise consists of the question related to sum, product and division of the complex numbers. **Question 1.** Evaluate :\\ (i) ${{i}^{31}}$ (ii) ${{\left(... }$ \\ [[math-11-nbf:sol:unit01:ex1-1-p1|Solution: Question 1]] **Question 2.** Write the following complex number in the form $x+iy$:\\ (i) $(3+2i)+(2+4i)$ (ii) $(4+
- Question 1, Exercise 1.3
- ====== Question 1, Exercise 1.3 ====== Solutions of Question 1 of Exercise 1.3 of Unit 01: Complex Numbers. This is unit of... ederal Textbook Board, Islamabad, Pakistan. ====Question 1(i)==== Factorize the polynomial into linear fun... (13i)^2 \\ = &(z + 13i)(z - 13i). \end{align} ====Question 1(ii)==== Factorize the polynomial into linear fu
- Question 6(i-ix), Exercise 1.4
- ====== Question 6(i-ix), Exercise 1.4 ====== Solutions of Question 6(i-ix) of Exercise 1.4 of Unit 01: Complex Numbers. Thi... deral Textbook Board, Islamabad, Pakistan. =====Question 6(i)===== Write a given complex number in the al... {i}{\sqrt{2}} \right) \\ =& 1-i. \end{align} =====Question 6(ii)===== Write a given complex number in the al
- Question 2, Exercise 1.1
- ====== Question 2, Exercise 1.1 ====== Solutions of Question 2 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of... ederal Textbook Board, Islamabad, Pakistan. ====Question 2(i)==== Write the following complex number in th... )\\ =&(3+2)+(i2+i4)\\ =&5+i6\end{align} GOOD ====Question 2(ii)==== Write the following complex number in t
- 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.... deral Textbook Board, Islamabad, Pakistan. =====Question 6(x)===== Write a given complex number in the alg... tion. ** //Do yourself as previous parts.// =====Question 6(xi)===== Write a given complex number in the al
- Question 8, Exercise 1.2
- ====== Question 8, Exercise 1.2 ====== Solutions of Question 8 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of... Federal Textbook Board, Islamabad, Pakistan. ====Question 8(i)==== Write $|2 z-i|=4$ in terms of $x$ and $y... 2+4y^2-4y-15=0, \end{align} as required. GOOD ====Question 8(ii)==== Write $|z-1|=|\bar{z}+i|$ in terms of $
- Question 9, Exercise 1.2
- ====== Question 9, Exercise 1.2 ====== Solutions of Question 9 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of... Federal Textbook Board, Islamabad, Pakistan. ====Question 9(i)==== Find real and imaginary parts of $(2+4 i... c{4}{20}\\ &= \dfrac{1}{5}. \end{align} GOOD ====Question 9(ii)==== Find real and imaginary parts of $(3-\
- Question 7, Exercise 1.4
- ====== Question 7, Exercise 1.4 ====== Solutions of Question 7 of Exercise 1.4 of Unit 01: Complex Numbers. This is unit of... deral Textbook Board, Islamabad, Pakistan. =====Question 7(i)===== Convert the following equation in Carte... mplies & x+y = 1. \end{align*} As required. =====Question 7(ii)===== Convert the following equations and in
- Question 3, Exercise 1.1
- ====== Question 3, Exercise 1.1 ====== Solutions of Question 3 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of... Federal Textbook Board, Islamabad, Pakistan. ====Question 3(i)==== Simplify the following $\dfrac{(2+i)(3-2... =&\dfrac{7}{2}-\dfrac{9}{2}i\end{align} GOOD ====Question 3(ii)==== Simplify the following $\dfrac{1+i}{(2+
- Question 10, Exercise 1.2
- ====== Question 10, Exercise 1.2 ====== Solutions of Question 10 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit ... Federal Textbook Board, Islamabad, Pakistan. ====Question 10(i)==== For $z_{1}=-3+2 i$, verify: $$\left|z_{... z_1} \right| = \sqrt{13}.$$ As required. GOOD ====Question 10(ii)==== For $z_{1}=-3+2 i$ and $z_{2}=1-3 i$ v
- Exercise 1.3 (Solutions)
- given on this page. This exercise consists of the question related to sum, product and division of the complex numbers. **Question 1.** Factorize the following polynomial into line... 11$\\ [[math-11-nbf:sol:unit01:ex1-3-p1|Solution: Question 1]] **Question 2.** Solve the following equation by completing square:\\ (i) $z^{2}-6 z+2=0$\\ (ii) $-\dfr
- Question 1, Exercise 1.1
- ====== Question 1, Exercise 1.1 ====== Solutions of Question 1 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of... Federal Textbook Board, Islamabad, Pakistan. ====Question 1(i)==== Evaluate ${{i}^{31}}$. **Solution.** \... -1\\ &=i\cdot(-1)\\ &=-i.\end{align} GOOD ====Question 1(ii)==== Evaulate ${{\left( -i \right)}^{6}}$.