+1804
We start off with the expression \((1+i) \over ( 2-i) (3+i) \)
Now, let's expand and simplify the bottom, we get \((1+i) \over ( 7 -i) \)
Now let's start the rationalization process. Multiply the top and bottom by the conjugate of the denominator, and we get
\(\frac{(1+i)}{ (7-i)} \cdot \frac{(7+i)}{(7+i)} \\ =\frac{6 +8i}{50}\)
Dividing top and bottom by 2 and canceling out the 2, we get
\(\frac{1}{25}( 3 + 4i) \) which is our final answer.
Thanks! :)
