Ответ:
Пошаговое объяснение:
1. Дано: Z₁ = 5 + 3i ; Z₂ = 8 - 4i .
z₁ + z₂ = ( 5 + 3i ) + ( 8 - 4i ) = 13 - i ;
z₁ - z₂ = ( 5 + 3i ) - ( 8 - 4i ) = - 3 + 7i ;
z₁ * z₂ = ( 5 + 3i ) * ( 8 - 4i ) = 40 - 20i + 24i - 12i² = 52 + 4i ;
z₁ /z₂ = ( 5 + 3i )/( 8 - 4i ) = ( 5 + 3i )*( 8 + 4i )/( 8 - 4i )*( 8 + 4i ) =
= ( 40 + 20i + 24i + 12i² )/( 64 - 16i² ) = ( 28 + 44i )/80 = 7/20 + 11/20 i .
2 . 1) i ¹² = ( i ⁴ )³ = 1³ = 1 ; 2) i ⁹⁶ = ( i ⁴ )²⁴ = 1²⁴ = 1 .
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Ответ:
Пошаговое объяснение:
1. Дано: Z₁ = 5 + 3i ; Z₂ = 8 - 4i .
z₁ + z₂ = ( 5 + 3i ) + ( 8 - 4i ) = 13 - i ;
z₁ - z₂ = ( 5 + 3i ) - ( 8 - 4i ) = - 3 + 7i ;
z₁ * z₂ = ( 5 + 3i ) * ( 8 - 4i ) = 40 - 20i + 24i - 12i² = 52 + 4i ;
z₁ /z₂ = ( 5 + 3i )/( 8 - 4i ) = ( 5 + 3i )*( 8 + 4i )/( 8 - 4i )*( 8 + 4i ) =
= ( 40 + 20i + 24i + 12i² )/( 64 - 16i² ) = ( 28 + 44i )/80 = 7/20 + 11/20 i .
2 . 1) i ¹² = ( i ⁴ )³ = 1³ = 1 ; 2) i ⁹⁶ = ( i ⁴ )²⁴ = 1²⁴ = 1 .