Inverse for Complex Multiplication/Examples/1+i

Example of Inverse for Complex Multiplication

$\dfrac 1 {1 + i} = \dfrac {1 - i} 2$

Proof

\(\ds \dfrac 1 {1 + i}\)

\(=\)

\(\ds \dfrac {1 - i} {\paren {1 + i} \paren {1 - i} }\)

multiplying top and bottom by $1 - i$

\(\ds \)

\(=\)

\(\ds \dfrac {1 - i} {1^2 + 1^2}\)

simplifying

\(\ds \)

\(=\)

\(\ds \dfrac {1 - i} 2\)

simplifying

$\blacksquare$