# How do you simplify # (5-i)/(2-i) - (3-7i)/(2-3i)# and write in a+bi form?

##### 1 Answer

#### Answer:

#### Explanation:

There are two different possibilities:

- either you combine the two fractions into one first and later write it in the
#a + bi# form - or you first write each of the fractions in
#a + bi# form and later subtract the one from the other

Which approach to pick is a matter of personal preference and doesn't make a big difference.

Let me do the second approach if you don't mind.

1) Transform

To do so, you need to make use of the formula

In order to achieve such a situation, you need to multiply both the numerator and the denominator with

... use

2) Transform

The approach is the same: multiply the numerator and the denominator with the conjugate of the denominator, namely

3) Subtract the two terms