Question

PRECISO DE AJUDA GALERA DOU 35 PONTOS!!FOTO EM BAIXO

Answer 1

1)

$Z=-8+2i\\W=5-i\\K=9-5i$

a)

$Z+K=(-8+2i)+(9-5i)=(9-8)+(2-5)i=1-3i$

b)

$Z-W=(-8+2i)-(5-i)=(-8-5)+(2+1)i=-13+3i$

c)

$\frac{W}{K}\\=\frac{5-i}{9-5i}\\=\frac{(5-i)(9+5i)}{(9-5i)(9+5i)}\\=\frac{1}{9^2+5^2}*(5-i)(9+5i)\\=\frac{1}{81+25}*[5*9-9i+5*5i-5i^2]\\ =\frac{1}{106}*(50+16i)\\ =\frac{1}{53}*(25+8i)$

d)

$K*Z=(9-5i)(-8+2i)\\=9*(-8)-5*(-8)*i+9*2i-5i*2i\\=-72+40i+18i-10i^2\\=-72+58i+10\\=-62+58i$

e)

$K+Z-W=(9-5i)+(-8+2i)-(5-i)=(9-8-5)+(-5+2+1)i=-4-2i$

2)

a)

$(3+2i^{22})i^{49}\\=(3+2(i^2)^{11})i^{2*24+1}\\=(3+2(-1)^{11})(i^2)^{24}*i\\=(3+2*(-1))*(-1)^{24}*i\\=(3-2)*i\\=i$

b)

$(-5+2i^{54})+(10-4i^{78})\\=(-5+2(i^2)^{27})+(10-4(i^2)^{39})\\=(-5+2(-1)^{27})+(10-4(-1)^{39})\\=(-5-2)+(10+4)\\=-7+14\\=7$

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