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don't understand how phi(a+c)=a+c. Please explain. Thank you

don't understand how phi(a+c)=a+c. Please explain. Thank you

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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I don't understand how phi(a+c)=a+c. Please explain. Thank you 

2:03 b) The objective is to check whether the given function : C→C is a ring homomorphism. Step 5/20 Consider the given function : C→C which is (a+bi) = a-bi defined by for all a, b in R To check whether the given function is ring homomorphism, it is enough to check the following two ring homomorphism conditions for all x, y in C i) (x + y) = (x) + (y) ii)(xy)=(x)o(y) lll 22% € Step 6/20 Check the first condition: $(x+y)= $(x)+ $(y) for all x, y in C Let x = a + bi and y=c+di, such that (x) = a - bi and (y)=c-di (x + y) = ((a+bi)+(c+di)) =p(a+c+(b+d)i) = (a + c)-(b+d)i
Transcribed Image Text:2:03 b) The objective is to check whether the given function : C→C is a ring homomorphism. Step 5/20 Consider the given function : C→C which is (a+bi) = a-bi defined by for all a, b in R To check whether the given function is ring homomorphism, it is enough to check the following two ring homomorphism conditions for all x, y in C i) (x + y) = (x) + (y) ii)(xy)=(x)o(y) lll 22% € Step 6/20 Check the first condition: $(x+y)= $(x)+ $(y) for all x, y in C Let x = a + bi and y=c+di, such that (x) = a - bi and (y)=c-di (x + y) = ((a+bi)+(c+di)) =p(a+c+(b+d)i) = (a + c)-(b+d)i
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