Exercise 1.1 (Solutions)

The solutions of the Exercise 1.1 of book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan are 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) ${{\left( -i \right)}^{6}}$ (iii) ${{\left( -1 \right)}^{\frac{-13}{2}}}$ (iv) $\dfrac{2}{(-1)^{\frac{3}{2}}}$ (v) $i^{23}+i^{58}+i^{21}$
Solution: Question 1

Question 2. Write the following complex number in the form $x+iy$:
(i) $(3+2i)+(2+4i)$ (ii) $(4+3i)-(2+5i)$ (iii) $(4+7i)+(4-7i)$
(iv) $(2+5i)-(2-5i)$ (v) $(3+2i)(4-3i)$ (vi) $(3,2)\div(3,-1)$
(vii) $(1+i)(1-i)(2+i)$ (viii) $\dfrac{1}{2+3i}$
Solution: Question 2

Question 3. Simplify the following :
(i) $\dfrac{(2+i)(3-2i)}{1+i}$ (ii) $\dfrac{1+i}{(2+i)^2}$ (iii) $\dfrac{1}{3+i}-\dfrac{1}{3-i}$
(iv) $(1+i)^{-2}+(1-i)^{-2}$ (v) $(2+i)^2+\dfrac{7-4i}{2+i}$(vi) $(3,2)\div(3,-1)$
Solution: Question 3

Question 4. Find the values of real number $x$ and $y$ in each of the following:
(i) $(2+3i)x+(1+3i)y+2=0$ (ii) $\dfrac{x}{(1+i)}+\dfrac{y}{1-2i}=1$
(iii) $\dfrac{x}{(2+i)}=\dfrac{1-5i}{(3-2i)}+\dfrac{y}{2-i}$ (iv) $x(1+i)^2+y(2-i)^2=3+10i$
Solution: Question 4

Question 5. Find the complex number $z$ if $4z-3\bar{z}=\dfrac{1-18i}{2-i}$
Solution: Question 5

Question 6. Find the conjugate of the following complex number :
(i) $4-3 i$ (ii) $3 i+8$ (iii) $2+\sqrt{\dfrac{-1}{5}}$ (iv) $\dfrac{5 }{2}i-\dfrac{7}{8}$
Solution: Question 6

Question 7. Find the magnitude of the following:
(i) $11+12 i$ (ii) $(2+3 i)-(2+6 i)$ (iii) $(2-i)(6+3 i)$ (iv) $\dfrac{3-2 i}{2+i}$ (v) $(\sqrt{3}-\sqrt{-8})(\sqrt{3}+\sqrt{-8})$
Solution: Question 7