1.Show that bar(z_1+z_2)=bar(z_1)+bar(z_2) 2.) Use Exercise 1 to show that bar(z^2)=(bar(z))^2 the z = a+bi bar(z)=a-bi bar(z_1)=a+bi

logosdepmpe

logosdepmpe

Answered question

2022-08-05

1.Show that z 1 + z 2 ¯ = z 1 ¯ + z 2 ¯
2.Use Exercise 1 to show that z 2 ¯ = ( z ¯ ) 2
the z=a+bi
z ¯ = a b i
z 1 ¯ = a + b i

Answer & Explanation

vladinognm

vladinognm

Beginner2022-08-06Added 13 answers

z=a+bi
( z 1 + z 2 ) = a 1 + a 2 + i ( b 1 + b 2 )
z 1 ¯ = a 1 b 1 i
z 2 ¯ = a 2 b 2 i
z 1 + z 2 ¯ = ( a 1 + a 2 ) i ( b 1 + b 2 )
z 1 ¯ + z 2 ¯ = ( a 1 + a 2 ) i ( b 1 + b 2 )
For second part:
z=a+bi
z ¯ = a b i
z 2 = ( a + b i ) ( a + b i ) = a 2 + 2 a b i b 2
z 2 ¯ = a 2 2 a b i b 2
( z ¯ ) = ( a b i ) ( a b i ) = a 2 2 a b i b 2

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