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(1) Using Euler's formula prove the following: a) For ZEC Sin²³² z + cos² z = 1 any b) For any 2₁, 2₂ € ( COS(7₁ +2₂) = COSZ, Cosz₂ - sinz, Siv 2₂ cos z =D if and only if z = T + TTK, KE ZZ ㅠ c) 2) Find all the solutions of the following equations Cif there is no solution write- no solution) Justify your answer Z (a) e ²-i = 0 b) e ²² = 1 c) 2²=²+1-i=0 3) a) Find the real and imaginary parts of the following functions: ^) f(2)= ²+1 2) f(z) = 3z² + 1/2

(1) Using Euler's formula prove the following: a) For ZEC Sin²³² z + cos² z = 1 any b) For any 2₁, 2₂ € ( COS(7₁ +2₂) = COSZ, Cosz₂ - sinz, Siv 2₂ cos z =D if and only if z = T + TTK, KE ZZ ㅠ c) 2) Find all the solutions of the following equations Cif there is no solution write- no solution) Justify your answer Z (a) e ²-i = 0 b) e ²² = 1 c) 2²=²+1-i=0 3) a) Find the real and imaginary parts of the following functions: ^) f(2)= ²+1 2) f(z) = 3z² + 1/2

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: 1 part c 2 part c 3 part a (question 2 of part a)
1) Using Euler's formula prove the following: a) For any ZEL sin²Z + cos² Z = 1 For any b) c) 2₁,2₂ € ( cos(7₁ +2₂) = COSZ, COSZ, - sinz, Sin 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 ²² = 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 ZEL sin²Z + cos² Z = 1 For any b) c) 2₁,2₂ € ( cos(7₁ +2₂) = COSZ, COSZ, - sinz, Sin 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 ²² = 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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