SOLUTION: EXPRESS 3+i/1+2i in the form a+bi where a and b are real numbers. {{{ (3+i)/(1+2i) }}}

EXPRESS 3+i/1+2i in the form a+bi where a and b
are real numbers.



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
which just equals 1 and will not change the value

·

Indicate multiplication of numerators and denominators:



FOIL out the top and bottom:



Combine like terms:



Replace  by 



Simplify



Combine like terms:



Make two fractions:



Simplify



Edwin