# 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 #