1) Using Euler's formula prove the following: a) For _Sin² Z + cos² z = 1 any ZEC b.) For any 2₁,7₂ € S c) CoS z = D COS (Z₁ + Z₂ ) = COSZ, Cost₂ - sinz, Sinz if and only if z = 2/1 + TTK, KE ZZ T 2) Find all the solutions of the following equations Cif there is no solution write- no solution) Justify your answer (a) e ²-i = 0 b) e ²² = 1 (c) 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
1) Using Euler's formula prove the following: a) For _Sin² Z + cos² z = 1 any ZEC b.) For any 2₁,7₂ € S c) CoS z = D COS (Z₁ + Z₂ ) = COSZ, Cost₂ - sinz, Sinz if and only if z = 2/1 + TTK, KE ZZ T 2) Find all the solutions of the following equations Cif there is no solution write- no solution) Justify your answer (a) e ²-i = 0 b) e ²² = 1 (c) 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
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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2c
3a2
Transcribed Image Text:(1) Using Euler's formula prove the following:
a) For any ZEC sin²Z + cos² Z = 1
For any
b)
c)
2₁,2₂ € ( COS(7₁ +2₂) = COSZ, COSZ₂ - 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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