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b). c) CoS z=D For any 2₁,7₂ €6. Cos(z₁ + Z₂) = Cosz, cost, - sinz, Shiz Z = 2 +TTK, KE ZZ T if and only if

b). c) CoS z=D For any 2₁,7₂ €6. Cos(z₁ + Z₂) = Cosz, cost, - sinz, Shiz Z = 2 +TTK, KE ZZ T if and only if

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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Questions: 1c 2c 3a2 (3z^2 + 1/z)
(1) Using Euler's formula prove the following: a) For any ZEI Sin ² z + Cos² Z = 1 For any b) c) 2₁,2₂ € ( COS(7₁ +2₂) = COSZ, COSZ₂ - sinz, Siv 2₂ cos z = D if and only if == 1/2 +TTK, KE ZZ ㅠ 2) Find all the solutions of the following equations Gif there is no solution write- no solution) Justify your answer Z a) e ²-i = 0 b) e ² = 1 c.) e ²² + 1 -i=0 3) a) Find the real and imaginary parts of the following functions: ^) f(2)= ²² +1₁ 소 2) f(z) = 3z² + 1/2
Transcribed Image Text:(1) Using Euler's formula prove the following: a) For any ZEI Sin ² z + Cos² Z = 1 For any b) c) 2₁,2₂ € ( COS(7₁ +2₂) = COSZ, COSZ₂ - sinz, Siv 2₂ cos z = D if and only if == 1/2 +TTK, KE ZZ ㅠ 2) Find all the solutions of the following equations Gif there is no solution write- no solution) Justify your answer Z a) e ²-i = 0 b) e ² = 1 c.) e ²² + 1 -i=0 3) a) Find the real and imaginary parts of the following functions: ^) f(2)= ²² +1₁ 소 2) f(z) = 3z² + 1/2
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