How do you simplify #(7+4i)/(2-3i)#?

1 Answer
Aug 12, 2016

Answer:

#2/13+29/13i#

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 - 3i

The 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#