Question

O módulo de i = $\sqrt{3}$ / $\sqrt{3}$ - i :

Answer 1

$z = \sqrt{3}/(\sqrt{3}-i)$
$z = \sqrt{3}*(\sqrt{3}+i)/[(\sqrt{3}-i)*(\sqrt{3}+i)]$
$z = (\sqrt{3}*\sqrt{3} + i\sqrt{3})/[(\sqrt{3})^{2}-i^{2})]$
$z = (3 + i\sqrt{3}) / (3 - [-1])$
$z = (3 + i\sqrt{3}) / (3 + 1)$
$z = (3 + i\sqrt{3}) / 4$
$z = (3 / 4) + (i\sqrt{3}/4)$
$z = (3/4) + (\sqrt{3}/4)i$
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$(|z|)^{2}=a^{2}+b^{2}$
$(|z|)^{2}=(3/4)^{2}+(\sqrt{3}/4)^{2}$
$(|z|)^{2}=(9/16)+(3/16)$
$(|z|)^{2}=(9+3)/16$
$(|z|)^{2}=12/16$
$(|z|)^{2}=3/4$
$|z|=\sqrt{3/4}$
$|z|= \sqrt{3}/\sqrt{4}$
$|z|=\sqrt{3}/2$