Review Exercise 1 (Solutions)

The solutions of the Review Exercise 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 polar form of the complex numbers.

Question 1. Choose the correct option.
Solution: Question 1

Question 2. Find the value of the following:
(i) $i^{2}+i^{4}+i^{6}+\cdots+i^{100}$
(ii) $\left|\dfrac{(3-2 i)(1+i)}{2-3 i}\right|$
(iii) $|\overline{(3-2 i)(4-i)}|$
(iv) $\left(\dfrac{3+5 i}{2-3 i}\right)^{-1}$
Solution: Question 2

Question 3. Factorize the following:
(i) $3 x^{2}+108$
(ii) $4 x^{2}+40$
Solution: Question 3

Question 4. Locate the complex number $z=x+i y$ on the complex plane if $\left|\dfrac{z+2 i}{z-2 i}\right|=1$
Solution: Question 4

Question 5. Find $z$ when $(z-3 i)(2+5 i)=3-4 i$.
Solution: Question 5

Question 6. Evaluate $\left[\dfrac{1}{i^{10}}+(2-i)^{2}+\sqrt{-25}\right]^{3}$
Solution: Question 6

Question 7. Solve by completing square method $2 z^{2}-11 z+16=0$.
Solution: Question 7

Question 8. When particle is at a position of $\sqrt{2}+i \sqrt{2}$nm from its mean position calculate its amplitude when $\theta=45^{\circ}$.
Solution: Question 8