Home | | Maths 12th Std | Exercise 2.7: Polar and Euler form of a Complex Number

Problem Questions with Answer, Solution - Exercise 2.7: Polar and Euler form of a Complex Number | 12th Mathematics : UNIT 2 : Complex Numbers

Chapter: 12th Mathematics : UNIT 2 : Complex Numbers

Exercise 2.7: Polar and Euler form of a Complex Number

Maths Book back answers and solution for Exercise questions - Mathematics : Complex Numbers: Polar and Euler form of a Complex Number: Exercise Questions with Answer, Solution

EXERCISE 2.7

1. Write in polar form of the following complex numbers

(i) 2 + i2√3

(ii) 3 - i√3

(iii) -2 - i2

(iv) i -1 / [cos (π/3) + i sin (π/3)].





2. Find the rectangular form of the complex numbers




3. If ( x1 + iy1 )( x2 + iy2 )( x3 + iy3 )... ...( xn + iyn ) = a + ib , show that

(i) (x12 + y12 )(x22 + y22 )(x32 + y32 )... ...(xn2 + y n2 ) = a2 + b2

(ii) 



4. If 1+ z / 1- z = cos 2θ + i sin 2θ , show that z = i tanθ .



5. If cos α + cos β + cos γ = sin α + sin β + sin γ = 0, show that

(i) cos 3α + cos 3β + cos 3γ = 3cos(α + β + γ ) and

(ii) sin 3α + sin 3β + sin 3γ = 3sin (α + β + γ ) .



6. If z = x + iy and arg ( z-i  / z+2) = π/4 , show that x2 + y2 + 3x - 3y + 2 = 0 .




Answers: 


Tags : Problem Questions with Answer, Solution , 12th Mathematics : UNIT 2 : Complex Numbers
Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail
12th Mathematics : UNIT 2 : Complex Numbers : Exercise 2.7: Polar and Euler form of a Complex Number | Problem Questions with Answer, Solution

Related Topics

12th Mathematics : UNIT 2 : Complex Numbers


Privacy Policy, Terms and Conditions, DMCA Policy and Compliant

Copyright © 2018-2023 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.