Question

What are the steps to simplify the expression 5+i/1+i

Answer 1

I assume you mean


`(5 + i)/(1 + i)`

although what you wrote means something else.

To get rid of the imaginary part in the denominator, you must multiply this fraction by a fraction which is the complex conjugate of the denominator over itself.
The denominator of the original fraction is 1 + i.
Its complex conjugate is 1 - i.
Multiply the original fraction by


`(1 - i)/(1 - i)`

Now we'll do it.


`(5 + i)/(1 + i) * (1 - i)/(1 - i) =`


`= ((5 + i)(1 - i))/((1 + i)(1 - i))`


`= (5 - 5i + i - i^2)/(1 - i^2)`


`= (5 - 4i - (-1))/(1 - (-1))`


`= (6 - 4i)/(2)`


`= 3 - 2i`