Write each of the functions in the form Aeat cos ßt+iBeat sin ßt, where a, B, A, and B are real numbers. (a) 2e²√2 (d) (√3e(1+¹1) ³ 2 (b) -(2+3i)t T (e) 21+1(1+ (c) —-—-e²¹+(1+x)
Write each of the functions in the form Aeat cos ßt+iBeat sin ßt, where a, B, A, and B are real numbers. (a) 2e²√2 (d) (√3e(1+¹1) ³ 2 (b) -(2+3i)t T (e) 21+1(1+ (c) —-—-e²¹+(1+x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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Please show all work and do all mentioned parts. Only do question 2 and only do sub parts of d and e.
![SES
-0.5
-1-
-1.5
-2
FIGURE 3.6
The graph of the solution found in Example 4, y(t) = 2 cos[t - (4π/3)].
1
2√2
10
The identity e²1+22= e²1e²2, from which we obtain (e)" = e", is useful in some of the
exercises.
(d) (√3e(¹+1¹)³
1. Write each of the complex numbers in the form a +iß, where a and ß are real
numbers.
(a) 2ein/3
(c) (2-1)¹3/2
(d)
e¹7π/6
(b)-2√2e-in/4
(e) (√žeix/6)4
2. Write each of the functions in the form Aeat cos ßt + iBeat sin ßt, where a, B, A, and
B are real numbers.
(a) 2e¹√2
(b) e
²e-(2+31)²
(e) (-²)'
л
(c)-½-²
--²1+i(1+x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71b114d5-6d72-4063-8215-3d54ecc2c41a%2F4e550fed-880a-4a21-916a-0d3657dc03be%2Fsaob9ww_processed.jpeg&w=3840&q=75)
Transcribed Image Text:SES
-0.5
-1-
-1.5
-2
FIGURE 3.6
The graph of the solution found in Example 4, y(t) = 2 cos[t - (4π/3)].
1
2√2
10
The identity e²1+22= e²1e²2, from which we obtain (e)" = e", is useful in some of the
exercises.
(d) (√3e(¹+1¹)³
1. Write each of the complex numbers in the form a +iß, where a and ß are real
numbers.
(a) 2ein/3
(c) (2-1)¹3/2
(d)
e¹7π/6
(b)-2√2e-in/4
(e) (√žeix/6)4
2. Write each of the functions in the form Aeat cos ßt + iBeat sin ßt, where a, B, A, and
B are real numbers.
(a) 2e¹√2
(b) e
²e-(2+31)²
(e) (-²)'
л
(c)-½-²
--²1+i(1+x)
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