How do you divide (6-i) / (1-i) ?

1 Answer
Jan 19, 2016

Explanation is given below.

Explanation:

For dividing complex numbers, you just need to multiply the numerator and denominator by the conjugate of the denominator.

If the complex number is a+ib then the conjugate is given by a-ib. color(red) "The imaginary term sign has to be changed"

In our problem (6-i)/(1-i)

The denominator is (1-i) remember for the conjugate we change the sign of the denominator.

The conjugate of 1-i is 1+i

So we have

(6-i)/(1-i)xx(1+i)/(1+i)

=((6-i)(1+i))/((1-i)(1+i))

=(6-6i-i+i^2)/(1^2-i^2)

=(6-7i-1)/(1-(-1))

=(7-7i)/(1+1)

=(7-7i)/2

=7/2 - 7/2i