Відповідь:
Покрокове пояснення:
z₁ = 3 - 4i ; z₂ = - 6 - 8i .
1) z₁ + z₂ = 3 - 4i + ( - 6 - 8i ) = 3 - 4i - 6 - 8i = - 3 - 12i ;
2) z₁ - z₂ = 3 - 4i - ( - 6 - 8i ) = 3 - 4i + 6 + 8i = 9 + 4i ;
3) z₁ * z₂ = ( 3 - 4i )( - 6 - 8i ) = - 18 - 24i 24i + 32i² = - 18 - 32 = - 50 ;
4) z₁/z₂ = ( 3 - 4i )/( - 6 - 8i ) = ( 4i - 3 )/( 6 + 8i ) = [ ( 4i - 3 )( 6 - 8i ) ]/[ ( 6 +
+ 8i )( 6 - 8i ) ] = ( 24i - 32i² - 18 + 24i )/( 6² - ( 8i )² ) =
= ( 48i + 32 - 18 )/( 36 - 64i² ) = ( 14 + 48i )/( 36 + 64 ) = ( 14 + 48i )/100 =
= 0,14 + 0,48i .
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Answers & Comments
Відповідь:
Покрокове пояснення:
z₁ = 3 - 4i ; z₂ = - 6 - 8i .
1) z₁ + z₂ = 3 - 4i + ( - 6 - 8i ) = 3 - 4i - 6 - 8i = - 3 - 12i ;
2) z₁ - z₂ = 3 - 4i - ( - 6 - 8i ) = 3 - 4i + 6 + 8i = 9 + 4i ;
3) z₁ * z₂ = ( 3 - 4i )( - 6 - 8i ) = - 18 - 24i 24i + 32i² = - 18 - 32 = - 50 ;
4) z₁/z₂ = ( 3 - 4i )/( - 6 - 8i ) = ( 4i - 3 )/( 6 + 8i ) = [ ( 4i - 3 )( 6 - 8i ) ]/[ ( 6 +
+ 8i )( 6 - 8i ) ] = ( 24i - 32i² - 18 + 24i )/( 6² - ( 8i )² ) =
= ( 48i + 32 - 18 )/( 36 - 64i² ) = ( 14 + 48i )/( 36 + 64 ) = ( 14 + 48i )/100 =
= 0,14 + 0,48i .