Maths Book back answers and solution for Exercise questions - Mathematics : Complex Numbers: de Moivreâ€™s Theorem and its Applications : Exercise problems with Questions, Answers, Solution, Explanation

EXERCISE 2.8

1. If Ï‰ â‰ 1 is a cube root of unity, show that

2. Show that

3. Find the value of

4. If 2cosÎ± = x + [1/x] and 2cos Î² = y + [1/y] , show that

5. Solve the equation z3 + 27 = 0 .

6. If Ï‰ â‰ 1 is a cube root of unity, show that the roots of the equation ( z -1)3 + 8 = 0 are -1, 1- 2Ï‰, 1- 2Ï‰2 .

7. Find the value of

8. If Ï‰ â‰ 1 is a cube root of unity, show that

(i) (1- Ï‰ + Ï‰2)6 + (1+ Ï‰ - Ï‰2 )6 = 128.

(ii) (1+ Ï‰ )(1+ Ï‰2)(1+ Ï‰4 )(1+ Ï‰8 )... ...(1+ Ï‰ 2.pow(11) ) = 1.

9. If z = 2 - 2i , find the rotation of z by Î¸ radians in the counter clockwise direction about the origin when

(i) Î¸ = Ï€/3

(ii) Î¸ = 2Ï€/3

(iii) Î¸ = 3Ï€ ./2

10. Prove that the values of 4âˆš-1 are Â± 1/âˆš2 (1Â±*i*).

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12th Mathematics : UNIT 2 : Complex Numbers : Exercise 2.8: de Moivreâ€™s Theorem and its Applications | Problem Questions with Answer, Solution | Complex Numbers

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