Exercise 1.3 (Solutions)

The solutions of the Exercise 1.3 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. Factorize the following polynomial into linear functions:
(i) $z^{2}+169$
(ii) $2 z^{2}+18$
(iii) $3 z^{2}+363$
(iv) $z^{2}+\dfrac{3}{25}$
(v) $2 z^{3}+3 z^{2}-10 z-15$
(vi) $z^{3}-7 z+6$
(vii) $z^{3}+2 z^{2}-23 z-60$
(viii) $2 z^{3}+9 z^{2}-11 z-30$
(ix) $z^{2}-7 z-8$
(x) $4 z^{2}-7 z-11$
Solution: Question 1

Question 2. Solve the following equation by completing square:
(i) $z^{2}-6 z+2=0$
(ii) $-\dfrac{1}{2} z^{2}-5 z+2=0$
(iii) $4 z^{2}+5 z=14$
(iv) $z^{2}=5 z-3$
Solution: Question 2

Question 3. Solve the following quadratic equation:
(i) $\dfrac{1}{3} z^{2}+2 z-16=0$
(ii) $z^{2}-\frac{1}{2} z+17=0$
(iii) $z^{2}-6 z+25=0$
(iv) $z^{2}-9 z+11=0$
Solution: Question 3

Question 4. Solve the following simultaneous system of linear equation with complex coefficients:
(i) $(1-i) z+(1+i) \omega=3 ; 2 z-(2+5 i) \omega=2+3 i$
(ii) $2 i z+(3-2 i) \omega=1+i ;(1-2 i) z+(3+2 i) \omega=5+6 i$
(iii) $\dfrac{3}{i} z-(6+2 i) \omega=5 ; \quad \dfrac{i}{2} z+\left(\dfrac{3}{4}-\dfrac{1}{2} i\right) \omega=\left(\dfrac{1}{2}+2 i\right)$
(iv) $\dfrac{1}{1-i} z+(1+i) \omega=3 ; \quad \dfrac{2}{i} z-(2-3 i) \omega=2+6 i$
Solution: Question 4