Question

6- Determine as seguintes operações: a) ( 3 – 2i ) – ( 1 - 4i ) b) ( 9 – 2i ) – ( 5 + 3i ) - ( 8 – 2 i ) c) ( 3 – 2i ) . ( 1 + 3i ) d) ( 1+ 2i ) . ( 5 + 3i ) .( 8 – i ) me ajudem por favor

Answer 1

Oie, Td Bom?!

a)

$= (3 - 2i) - (1 - 4i)$

$= 3 - 2i - 1 + 4i$

$= 2 + 2i$

b)

$= (9 - 2i) - (5 + 3i)$

$= 9 - 2i - 5 - 3i$

$= 4 - 5i$

c)

$= (3 - 2i) \: . \: (1 + 3i)$

$= 3(1 + 3i) - 2i \: . \: (1 + 3i)$

$= 3 + 9i - 2i - 6i {}^{2}$

$= 3 + 9i - 2i - 6 \: . \: ( - 1)$

$= 3 + 9i - 2i + 6$

$= 9 + 7i$

d)

$= (1 + 2i) \: . \: (5 + 3i) \: . \: (8 - i)$

$= (5i + 3i + 10i + 6i {}^{2} ) \: . \: (8 - i)$

$= (5 + 3i + 10i + 6 \: . \: ( - 1)) \: . \: (8 - i)$

$= (5 + 3i + 10i - 6) \: . \: (8 - i)$

$= ( - 1 + 13i) \: . \: (8 - i)$

$= - 8 + i + 104i - 13i {}^{2}$

$= - 8 + i + 104i - 13 \: . \: ( - 1)$

$= - 8 + i + 104i + 13$

$= 5 + 105i$

Att. Makaveli1996

Answer 2

Explicação passo-a-passo:

a)

(3 - 2i) - (-1 - 4i)

= 3 - 2i -1 + 1 + 4i

= 3 - 1 - 2i + 4i

= 2 + 2i

b)

(9 - 2i) - (5 + 3i) - (8 - 2i)

= 9 - 2i - 5 - 3i - 8 + 2i

= 9 - 5 - 8 - 2i - 3i + 2i

= -4 - 3i

c)

(3 - 2i).(1 + 3i)

= 3 + 9i - 2i - 6i²

= 3 + 9i - 2i - 6.(-1)

= 3 + 9i - 2i + 6

= 3 + 6 + 9i - 2i

= 9 + 7i

d)

(1 + 2i).(5 + 3i).(8 - i)

= (5 + 3i + 10i + 6i²).(8 - i)

= (5 + 3i + 10i - 6).(8 - i)

= (-1 + 13i).(8 - i)

= -8 + i + 104i - 13i²

= -8 + i + 104i - 13.(-1)

= -8 + i + 104i + 13

= -8 + 13 + i + 104i

= 5 + 105i