How do you simplify #(7+4i)/(2-3i)#?
1 Answer
Aug 12, 2016
Explanation:
To simplify this fraction we have to make the denominator real.
To do this multiply the numerator and denominator by the
#color(blue)"complex conjugate"# of 2 - 3iThe conjugate of 2 - 3i is 2 + 3i
Note that
#(2-3i)(2+3i)=13" a real number"# Multiply numerator/denominator by 2 + 3i
#((7+4i)(2+3i))/((2-3i)(2+3i))=(14+29i+12i^2)/13=(2+29i)/13#
#rArr(7+4i)/(2-3i)=2/13+29/13i#
