Question 390122
<pre><font size = 4 color = "indigo" face = "batangche"><b>

{{{1/((a+bi))}}}

Multiply by the conjugate of the denominator over itself:

{{{expr(1/((a+bi)))expr(((a-bi))/((a-bi))) )}}}

Multiply numerator and denominator:

{{{(a-bi)/((a+bi)(a-bi))}}}

FOIL out the bottom and simplify:

{{{(a-bi)/(a^2-abi+abi-b^2i^2)}}}

{{{(a-bi)/(a^2-b^2i^2)}}}

replace iČ by (-1) and simplify:

{{{(a-bi)/(a^2-b^2(-1))}}}

{{{(a-bi)/(a^2+b^2)}}}

If you want to write it in the form A+Bi,

{{{(a/(a^2+b^2))-(expr(b/(a^2+b^2)))*i}}}

Edwin</pre>