Question

Efetue as operações indicadas escrevendo o resultado na forma algébrica Z=a+bi.?
a)(1/2 + 2i) (1/3 - 3i)

b) (1+i) (1+i)³ (1+i) elevado a -1

c) 3(7+2i) - [(5+4i) + 1)]

Answer 1

Explicação passo-a-passo:

a)

$Z=(\frac{1}{2}+2i).(\frac{1}{3} -3i)\\ \\Z=\frac{1}{2} .\frac{1}{3} +\frac{1}{2}.(-3i)+2i.\frac{1}{3} +2i.(-3i)\\\\Z=\frac{1}{6} -\frac{3i}{2} +\frac{2i}{3} -6i^{2} \\\\Z=\frac{1}{6}-\frac{9i}{6}+\frac{4i}{6} -6.(-1)\\\\Z=6+\frac{1}{6}-\frac{5i}{6}\\\\Z=\frac{37}{6} -\frac{5}{6}i$

b)

$Z=(1+i).(1+i)^{3} .(1+i)^{-1} =(1+i)^{1+3-1} =(1+i)^{3} \\\\Z=1^{3}+3.1^{2}.i +3.1.i^{2} +i^{3} \\\\Z=1+3i+3i^{2} +i^{2}.i \\\\Z=1+3i-3-i\\\\Z-2+2i$

c)

$Z=3.(7+2i)-[(5+4i)+1]\\\\Z=21+6i-[6+4i]\\\\Z=21+6i-6-4i\\\\Z=15+2i$