How do you simplify #5/(3-4i)#?
To simplify this fraction, we require the denominator to be real.
To achieve this multiply both the numerator and denominator by the
#color(blue)"complex conjugate"#of the denominator.
Given z = a ± bi then the conjugate is
Note that the real part remains unchanged while the sign of the imaginary part is reversed.
#color(red)(|bar(ul(color(white)(a/a)color(black)((a+bi)(a-bi)=a^2)color(white)(a/a)|)))" the result is real"#
where a and b are real.
#rArr3-4i" has conjugate " 3+4i#
multiply numerator/denominator by (3+4i)