Let z = r+yi, x, Y E R. Which of the following equality hold(s)? (a) cos(r + iy) = cos r cos y – sin r sin y (b) cos(r+ iy) = cos I cosh y – sin x sinh y (c) cos(r + iy) = cos I cosh y – i sin a sinh y (d) cos(x+ iy) = cos x cos y – i sin r sin y where for y E R, 1 cosh y = (e" + e=") 1 sinh y = (e" – e") 3.
Let z = r+yi, x, Y E R. Which of the following equality hold(s)? (a) cos(r + iy) = cos r cos y – sin r sin y (b) cos(r+ iy) = cos I cosh y – sin x sinh y (c) cos(r + iy) = cos I cosh y – i sin a sinh y (d) cos(x+ iy) = cos x cos y – i sin r sin y where for y E R, 1 cosh y = (e" + e=") 1 sinh y = (e" – e") 3.
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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[Complex Variables] Which equality holds?
Transcribed Image Text:Let z = r+yi, x, Y E R. Which of the following equality hold(s)?
(a) cos(r + iy) = cos r cos y – sin r sin y
(b) cos(r+ iy) = cos I cosh y – sin x sinh y
(c) cos(r + iy) = cos I cosh y – i sin a sinh y
(d) cos(x+ iy) = cos x cos y – i sin r sin y
where for y E R,
1
cosh y = (e" + e=")
1
sinh y = (e" – e")
3.
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