There are two forms for complex numbers, rectangular (a+bi) and trigonometric
form r∙cis(q).  

Rectangular form is easy to add and subtract but hard to multiply and divide.
Trigonometric form is easy to multiply and divide but hard to add and subtract. 

So we will change A and B to rectangular form and add them





We use our knowledge of sines and cosines of special angles 30° and 45°, to substitute for them:



We distribute to remove parentheses:

 

We swap the middle two terms to get the real terms together and the
imaginary terms together:

 

Put parentheses around the real terms and factor out i from the imaginary terms:

 

You may leave it like that. Or, since the deminators are the same, you may combine the numerators over the common denominator



Edwin