Question 315483
Write the following expressions as a complex number in standard form.
{{{(-1+5i)/(3+7i)}}}
<pre><b>
Form the conjugate of {{{3+7i}}} by changing the sign of the term
containing {{{i}}} and leaving the sign of the first term.

Thus the conjugate of {{{3+7i}}} is {{{3-7i}}}.

Place that conjugate over itself, like this {{{((3-7i)/(3-7i))}}},
which just equals 1, and so we can now multiply the original
expression by that without changing its value:

{{{((-1+5i)/(3+7i))}}}{{{((3-7i)/(3-7i))}}}

{{{( (-1+5i)(3-7i) ) / ( (3+7i)(3-7i) )}}}

Using FOIL on top and bottom:

{{{ (-3+7i+15i-35i^2)/(9-21i+21i-49i^2)}}}

Combining like terms (the middle terms cancel in the bottom)

{{{ (-3+22i-35i^2)/(9-49i^2)}}}

Replace {{{i^2}}} by {{{-1}}}

{{{ (-3+22i-35(-1))/(9-49(-1))}}}

Simplify:

{{{ (-3+22i+35)/(9+49)}}}

{{{ (32+22i)/58}}}

Make two fractions, and write the {{{i}}} as multiplied on the right of
the second fraction, so it will be in the standard form {{{A+Bi}}}:

{{{32/58}}}{{{"+"}}}{{{22/58}}}{{{i}}}

Reduce the fractions

{{{16/29}}}{{{"+"}}}{{{11/29}}}{{{i}}}

Edwin</pre>