Compute the following: a. (2+5)* b. (4-3i)¹/6 c. Simplify: cos 50+isin50 cos 40+isin40 d. If z = cos 0 + isinė, show that z + ² = 2cos 6
Compute the following: a. (2+5)* b. (4-3i)¹/6 c. Simplify: cos 50+isin50 cos 40+isin40 d. If z = cos 0 + isinė, show that z + ² = 2cos 6
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
![1Q. Compute the following:
a. (2+5)*
b. (4-3i)¹/6
cos 40+isin40
c. Simplify: cos 50+isin 50
d. If z = cos 0 + isinė, show that z + = = 2cos 0
2Q. Find the first four terms in each portion of the series solution around x = 0 for the
following differential equation.
x²y" − 5x y' + 6y = 0
3Q. Find a series solution around x = 0 for the following differential equation.
y" - 4y = 0
4Q. Determine the Fourier series for the following functions:
a. Let f(x) be an 27-periodic function such that f(x) = x for x € [-^,^]. Find the
Fourier series for the parabolic wave.
b. Find the Fourier Series for the square wave:
1
f (x) =
(a) f(t) =
if 0 < x < π
if π < x≤ 2π
5Q. Laplace transform of the following functions:
sin 2t
t
(b) f(t) = 7t²e-3t
(c) f(t) = 3tan 4t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde86deda-7e01-4b7e-8b80-769cb7e2f571%2F78c4178d-3573-4df1-81dd-82e45719b3a6%2Fu2lh6rb_processed.png&w=3840&q=75)
Transcribed Image Text:1Q. Compute the following:
a. (2+5)*
b. (4-3i)¹/6
cos 40+isin40
c. Simplify: cos 50+isin 50
d. If z = cos 0 + isinė, show that z + = = 2cos 0
2Q. Find the first four terms in each portion of the series solution around x = 0 for the
following differential equation.
x²y" − 5x y' + 6y = 0
3Q. Find a series solution around x = 0 for the following differential equation.
y" - 4y = 0
4Q. Determine the Fourier series for the following functions:
a. Let f(x) be an 27-periodic function such that f(x) = x for x € [-^,^]. Find the
Fourier series for the parabolic wave.
b. Find the Fourier Series for the square wave:
1
f (x) =
(a) f(t) =
if 0 < x < π
if π < x≤ 2π
5Q. Laplace transform of the following functions:
sin 2t
t
(b) f(t) = 7t²e-3t
(c) f(t) = 3tan 4t
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