How do you simplify #1/(2+3i)#?

2 Answers
Jun 16, 2018

Answer:

#1/(2+3i)=2/13-3/13i#

Explanation:

#1/(2+3i)# is reciprocal of complex number #2+3i#. To find reciprocal we multiply numerator and denominator each by complex conjugate of #2+3i#, which is #2-3i#. Hence,

#1/(2+3i)=1/(2+3i)×(2-3i)/(2-3i)#

= #(2-3i)/(2^2-(3i)^2)#

= #(2-3i)/(4-9i^2)#

= #(2-3i)/(4+9)#

= #2/13-3/13i#

Jun 16, 2018

Answer:

#2/13-3/13i#

Explanation:

#"multiply the numerator/denominator by the complex"#
#"conjugate of the denominator"#

#"the conjugate of "2+3i" is "2color(red)(-)3i#

#(2+3i)(2-3i)=2^2-9i^2=4+9=13#

#=(2-3i)/13=2/13-3/13ilarrcolor(blue)"in standard form"#