Why we cannot divide 3+5i by 1+i?

The answer is
easy!

The divisor 1 + i cannot divide 3 + 5i because it is
not a real number. The division of complex numbers follows the next procedure. First,
we'll have to multiply both numerator and denominator by the conjugate of
divisor.

((3+5i)(1-i))/((1+i)(1-i))

We notice that the special
product from denominator returns a difference of two
squares:

((3+5i)(1-i))/2

Since the divisor is a real number we can
perform now the division.

We'll remove the brackets from
numerator:

5i^2)/2

5)/2

 
2i)/2

i))/2

 
i

The result of division of the complex
numbers 3 + 5i and 1 + i is the complex number 4 +
i.