How do you simplify #3/(6-3i)#?
1 Answer
Oct 20, 2016
Explanation:
To simplify this fraction, we must multiply the numerator/denominator by the
#color(blue)"complex conjugate"# of the denominator.
This ensures that the denominator is a real number.Given a complex number
#z=x±yi# then the complex conjugate is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(barz=x∓yi)color(white)(2/2)|)))# Note that the real part remains unchanged while the
#color(red)"sign"# of the imaginary part is reversed.Hence the conjugate of
#6-3i" is " 6+3i# and
#(6-3i)(6+3i)=36+9=45larr" a real number"#
#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(i^2=(sqrt(-1))^2=-1)color(white)(2/2)|)))# Multiply numerator/denominator by 6 + 3i
#(3(6+3i))/((6-3i)(6+3i))=(18+9i)/45=18/45+9/45i=2/5+1/5i#