Question

z=1+√2 i,escreva na forma algébrica , o complexo Z -¹

Answer 1

$|z|= \sqrt{a^2+b^2} \\ |z|= \sqrt{1+2}= \sqrt{3} \\ \\ Senx= \frac{\sqrt{2}}{ \sqrt{3} }=\frac{\sqrt{6}}{3} \\ \\ Cosx\frac{1}{ \sqrt{3}}= \frac{ \sqrt{3} }{3} \\ z=a+bi \\\\a=Senx.|z|.i \\b=Cosx.|z|\\z=Senx.|z|+Cosx.|z|\\z=|z|(Senx+Cosx) \\ \\z= \sqrt{3}( \frac{ \sqrt{6} }{3}.i+ \frac{ \sqrt{3} }{3})$