Question

efetue as divirsoes indicadas:

a) 2+3i/1+3i

b) 1/3+5i

c) 1+2i/3i​

Answer 1

Resposta:

Explicação passo a passo:

Efetue as divirsoes indicadas:

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

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

= (2-6i+3i -9i^2)/(1 - 9i^2)

=(2-3i -9i^2)/(1-9i^2)

= [2-3i -9.(-1)]/ [1-9.(-1)]

= [2 - 3i + 9] / (1+9)

= [11 - 3i]/10

= 11/10 - 3i/10

_____________

b)

= 1/(3+5i) . (3-5i)/(3-5i)

= (3-5i)/(3+5i).(3-5i)

= (3-5i)/(9-25i^2)

=(3-5i) / [9-25.(-1)]

= (3-5i)/(9+25)

= (3-5i)/34

= 3/34 - 5i/34

________

c) (1+2i)/3i​ . 3i/3i

= 3i.(1+2i) / 3i.3i

= (3i+6i^2) /9i^2

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

= (3i - 6)/(-9)

= (-3i +6)/9

= -3i/9 (:3)/(:3) + 6/9 (:3)/(:3)

= - i/3 + 2/3