I assume you mean the number
(1 + i) / (3 + i)
Multiply the numerator and denominator by the complex conjugate of 3 + i, which is 3 - i :
(1 + i) / (3 + i) • (3 - i) / (3 - i)
Recall the difference of squares identity,
a² - b² = (a + b) (a - b)
which makes the denominator of the product simplify to
(3 + i) (3 - i) = 3² - i² = 9 + 1 = 10
and so
(1 + i) / (3 + i) = (1 + i) (3 - i) / 10
Expand the numerator:
(1 + i) (3 - i) = 3 + 2i - i² = 4 + 2i
Then
(1 + i) / (3 + i) = (4 + 2i) / 10 = 2/5 + i 1/5
