Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. algebra
  3. 1 8 2 show that cos z cos x sinh y where x iy find

1 8 2 Show that cos z cos x sinh y where x iy Find...

50.1K

Verified Solution

Question

Algebra

image

1 8 2 Show that cos z cos x sinh y where x iy Find all zeros and periods of cos z Solution Use trigonometric formulas from page 29 and 30 in CA we have cos z cos x iy cos rcos iy sin r sin iy cos x cosh y i sin x sinh y Now take the modulus squared and use cosh y 1 sinh y cos 2 cos r cosh y sin x sinh y cos r 1 sinh y sin r sinh y cos r cos r sin r sinh y cos r sinhy The identity for cos 22 shows that the only zeros of cos z are the zeros of cos on the real axis because cos z 0 cos x 0 r 1 ma m 0 1 2 Translation by any period A of cos z sends zeros to zeros Thus any period is an integral multiple of and since odd integral multiples are not periods the only periods of cos z are 2an 0 n

Answer & Explanation Solved by verified expert
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students