Пошаговое объяснение:
1 . z₁ = 1/2 - 1/3 i ; z₂ = 1 + 3i ;
1) z₁ + z₂ = 1/2 - 1/3 i + 1 + 3i = 1 1/2 + 2 2/3 i ;
2) z₁ - z₂ = 1/2 - 1/3 i - 1 - 3i = - 1/2 - 3 1/3 i ;
3) z₁ / z₂ = (1/2 - 1/3 i )/( 1 + 3i ) = [(1/2 - 1/3 i )( 1 - 3i )]/[( 1 + 3i )( 1 - 3i ) ] =
= ( - 1/2 - 1 1/6 i )/( 1² - (3i )²) = ( - 1/2 - 1 1/6 i )/( 1 + 9 ) = ( - 1/2 - 1 1/6 i )/10 =
= - 1/20 - 7/60 i .
Пошаговое объяснение:
1 . z₁ = 1/2 - 1/3 i ; z₂ = 1 + 3i ;
1) z₁ + z₂ = 1/2 - 1/3 i + 1 + 3i = 1 1/2 + 2 2/3 i ;
2) z₁ - z₂ = 1/2 - 1/3 i - 1 - 3i = - 1/2 - 3 1/3 i ;
3) z₁ / z₂ = (1/2 - 1/3 i )/( 1 + 3i ) = [(1/2 - 1/3 i )( 1 - 3i )]/[( 1 + 3i )( 1 - 3i ) ] =
= ( - 1/2 - 1 1/6 i )/( 1² - (3i )²) = ( - 1/2 - 1 1/6 i )/( 1 + 9 ) = ( - 1/2 - 1 1/6 i )/10 =
= - 1/20 - 7/60 i .