Question

determine o inverso de z=1-2i

Answer 1

$z=1-2i$

$z^{-1} = \frac{1}{1-2i} = \frac{1.(1+2i)}{(1-2i).(1+2i)} = \frac{1+2i}{ 1^{2} - (2i)^{2} } = \frac{1+2i}{ 1 - 4i^{2} } = \frac{1+2i}{ 1 - 4.(-1) } = \frac{1+2i}{ 1 +4 } = \frac{1+2i}{ 5 }$