How do you divide # (6-i) / (7-2i) #?
1 Answer
Apr 8, 2016
Explanation:
To divide this fraction we require to rationalise the denominator.
We do this by multiplying numerator/denominator by the
#color(blue)" complex conjugate " " of the denominator " # If
#color(blue)" a ± bi " " is a complex number then " #
# color(red)" a ∓ bi " " is it's conjugate " # Note that the 'real part' remains unchanged , while the sign of the 'imaginary part' changes.
Also (a+ bi)(a - bi) =
# a^2 - b^2 " a real number " # and
# i^2 = (sqrt(-1))^2 = -1 # Now the conjugate of 7 - 2i is 7 + 2i
multiplying numerator / denominator by (7 + 2i)
#rArr ((6 - i)(7 + 2i))/((7 - 2i)(7 + 2i)) = (42 + 5i +2)/(49 + 4)= 44/53 + 5/53 i #
