How do you divide (6-i) / (7-2i) 6−i7−2i?
1 Answer
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 " complex conjugate of the denominator If
color(blue)" a ± bi " " is a complex number then " a ± bi is a complex number then
color(red)" a ∓ bi " " is it's conjugate " 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 " a2−b2 a real number and
i^2 = (sqrt(-1))^2 = -1 i2=(√−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 ⇒(6−i)(7+2i)(7−2i)(7+2i)=42+5i+249+4=4453+553i
