badge image

Enroll For Free Now & Improve Your Performance.

User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.

Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: Rs.

There are no items in this cart.
Continue Shopping


cos(1-i) = a+ib (a,b are reals), then which is correct a) a=1\2(e - 1\e)cos1, b=1\2(e+ 1\e)sin1 b) a=1\2(e + 1\e)cos1, b=1\2(e - 1\e)sin1 c) a=1\2(e + 1\e)cos1, b=1\2(e+ 1\e)sin1 d) a=1\2(e - 1\e)cos1, b=1\2(e-1\e)sin1

11 years ago

Answers : (1)

Ramesh V
70 Points

we know that : e^(ix)=cos x + i sin x

so e(ix)=cos x + i sin x

     e-(ix)=cos x - i sin x  where x is: A+iB

so we can write:   cos(A+iB)=1/2(ei(A+iB) +e-i(A+iB))

here A=1 and B=-1

so 1/2(ei(1-i1) +e -i(1-i1))=a+ib

     1/2(ei+1 +e -i-1)=a+ib

     1/2(ei.e +e-1e -i  )=a+ib where ( ei= cos 1+i sin 1)

     e/2( cos 1+i sin1)+1/2e(cos 1-i sin1) = a+ ib

    1/2 (ecos 1+1/e.cos1)+i/2(e.sin1-1/e.sin1) = a+ ib

 equating real and imaginery parts, we'll get


a=1/2 cos 1(e+e-1)

b=1/2 sin 1(e-e-1)


the answer is B





11 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution

Course Features

  • 101 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!! Click Here for details