Question 67184
<pre><font size = 5><b>EXPRESS 3+i/1+2i in the form a+bi where a and b
are real numbers.

{{{ (3+i)/(1+2i) }}}

The conjugate of the denominator is formed by
copying it but changing the sign of the coeffcient
of i. Therefor the conjugate of 1+2i is 1-2i. So
we multiply by the fraction{{{(1-2i)/(1-2i)}}}
which just equals 1 and will not change the value

{{{ (3+i)/(1+2i) }}}·{{{ (1-2i)/(1-2i) }}}

Indicate multiplication of numerators and denominators:

{{{ ((3+i)(1-2i))/((1+2i)(1-2i)) }}}

FOIL out the top and bottom:

{{{ (3-6i+i-2i^2)/(1-2i+2i-4i^2) }}}

Combine like terms:

{{{ (3-5i-2i^2)/(1-4i^2) }}}

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

{{{ (3-5i-2(-1))/(1-4(-1)) }}}

Simplify

{{{(3-5i+2)/(1+4)}}}

Combine like terms:

{{{(5 - 5i)/5}}}

Make two fractions:

{{{5/5 - 5i/5}}}

Simplify

{{{1 - i}}}

Edwin</pre>