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2. Write each of the functions in the form Aet cos Bt +iBed sin Bt, where a, B, A, and B are real numbers. (a) 2eiv2i 2 -(2+3i)t (b) =e 1 (c) 3 1 (e)

2. Write each of the functions in the form Aet cos Bt +iBed sin Bt, where a, B, A, and B are real numbers. (a) 2eiv2i 2 -(2+3i)t (b) =e 1 (c) 3 1 (e)

Advanced Engineering Mathematics
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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section 3.5

The identity ei+2 = e²1e²2, from which we obtain (e?)" = e, is useful in some of the exercises. 1. Write each of the complex numbers in the form a +iB, where a and B are real numbers. (a) 2ein/3 (b) –2/2e-i/4 (c) (2 – i)e37/2 1 (d) : e'7x/6 (e) (VZer/6)* 2/2 2. Write each of the functions in the form Ae" cos Bt +iBeat sin Bt, where a, ß, A, and B are real numbers. (a) 2eiv2t 2 -(2+3i)t (b) 1 21+i(f+x) (c) (d) (/Že"+*)³ 3 (e) eint
Transcribed Image Text:The identity ei+2 = e²1e²2, from which we obtain (e?)" = e, is useful in some of the exercises. 1. Write each of the complex numbers in the form a +iB, where a and B are real numbers. (a) 2ein/3 (b) –2/2e-i/4 (c) (2 – i)e37/2 1 (d) : e'7x/6 (e) (VZer/6)* 2/2 2. Write each of the functions in the form Ae" cos Bt +iBeat sin Bt, where a, ß, A, and B are real numbers. (a) 2eiv2t 2 -(2+3i)t (b) 1 21+i(f+x) (c) (d) (/Že"+*)³ 3 (e) eint
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