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2. By writing /12 = (7/3)-(7/4) and considering e/12,evaluate cot(7/12) and tan(z/12).

2. By writing /12 = (7/3)-(7/4) and considering e/12,evaluate cot(7/12) and tan(z/12).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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O ..L O 51% 6:59 PM 24 CHAPTER 1. INTRODUCTION TO NUMBER THEORY 2. By writing /12 = (T/3)-(7/4) and considering er/12 evaluate cot(T/12) and tan(a/12). 3. Use de Moivres theorem with n = 4 to prove that cos40 = 8cos 0 – 8cos 0 +1 4. Use de Moivres theorem to prove that tan50 = M where t = tand 5. Evaluate (a) i (b) Im2+3 (c) erp(i) (d) (-1+ v3i)1/2 (e) edin +1 (f) (1+ i)1000 6. Find the cubic roots of a complex number z = -1+i 7. Find the cubic roots of unity 8. Show that log z" =log [(re") 9. Show that log (e*) = z 10. If z = a – ib, what is iz 11. Simplify z = (25i)(3 + i)/(3i) and find the modulus and argument of the result 12. If w = = and :=r+ iy and w = u + iv, find u and v. 13. If i = -1, what are ,",. 14. If z = 3+ 41 find 2 and the modulus and argument of 2? 15. Find z" if 0 =T and r = 2. 16. Write (V5)ettan-() in the form a + bi.
Transcribed Image Text:O ..L O 51% 6:59 PM 24 CHAPTER 1. INTRODUCTION TO NUMBER THEORY 2. By writing /12 = (T/3)-(7/4) and considering er/12 evaluate cot(T/12) and tan(a/12). 3. Use de Moivres theorem with n = 4 to prove that cos40 = 8cos 0 – 8cos 0 +1 4. Use de Moivres theorem to prove that tan50 = M where t = tand 5. Evaluate (a) i (b) Im2+3 (c) erp(i) (d) (-1+ v3i)1/2 (e) edin +1 (f) (1+ i)1000 6. Find the cubic roots of a complex number z = -1+i 7. Find the cubic roots of unity 8. Show that log z" =log [(re") 9. Show that log (e*) = z 10. If z = a – ib, what is iz 11. Simplify z = (25i)(3 + i)/(3i) and find the modulus and argument of the result 12. If w = = and :=r+ iy and w = u + iv, find u and v. 13. If i = -1, what are ,",. 14. If z = 3+ 41 find 2 and the modulus and argument of 2? 15. Find z" if 0 =T and r = 2. 16. Write (V5)ettan-() in the form a + bi.
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