Question

Ajuda em matemática ::: 10pontos

Answer 1

$\boxed{\boxed{i^{2}=-1}}~~~\therefore~~~\boxed{\boxed{i^{4}=1}}$
_______________________________

Deixando z na forma algébrica:

$z=5i+3i^{2}-2i^{3}+4i^{27}\\z=5i+3(-1)-2i^{2}i^{1}+4(i^{4})^{6}i^{2}i\\z=5i-3-2(-1)i+4(1)^{6}(-1)i\\z=5i-3+2i-4i\\z=-3+3i$

Deixando w na forma algébrica:

$w=2i^{12}-3i^{15}\\w=2(i^{4})^{3}-3(i^{4})^{3}i^{2}i\\w=2(1)^{3}-3(1)^{3}(-1)i\\w=2-(-3)i\\w=2+3i$

Logo, vemos que:

$Im(z)=3\\Im(w)=3$
____________________________

$Im(z).w+Im(w).z=3(2+3i)+(-3+3i)3\\Im(z).w+Im(w).z=3(2+3i-3+3i)\\Im(z).w+Im(w).z=3(-1+6i)\\Im(z).w+Im(w).z=-3+18i$