Question

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

Answer 1

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`