How do you rationalize #4/(2-3i)#?

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Answer 1 · 2018-03-18T18:39:59

#(8+12i)/(13)#

the difference of two squares identity,

#(a+b)(a-b) = a^2-b^2#,

can be used to rationalise the #a+bi# expression.

to rationalise the denominator, multiply it by its conjugate.

the conjugate is found by changing the #-# sign to #+#.

here, it is #2+3i#.

if both the numerator and denominator are multiplied by #2+3i:#

#4 * (2+3i) = 8 + 12i#

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

#= 4 - (-9) = 4 + 9#

#=13#

therefore, the equivalent fraction to #(4)/(2-3i)# where the denominator is rational, is #(8+12i)/(13)#.