How do you simplify # (5-i)/(2-i) - (3-7i)/(2-3i)# and write in a+bi form?
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.
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
The approach is the same: multiply the numerator and the denominator with the conjugate of the denominator, namely
3) Subtract the two terms