Simplifying solution to algebraic system of equations

The following code outputs a value for a and b with respect to the imaginary number i but the output is not fully simplified with the complex and real part separately factored. Is there a way to modify the code so the real and imaginary parts are separate?

syms X Y Q t w v a b  z c N theta m L g  
eq1 = b-a == 10*(cosd(45)+i*sind(45)); 
eq2 = 3 == (a-b)/4+a*i/3 + b/(6*i)+b/12; 

sol = solve([eq1 eq2], [b a]); %[a b c] = [theta' theta'' x'']
 
sol_b = simplify(sol.b)
solb = sol.b

Answer 1

[John D'Errico]

It would be almost as easy to solve by hand.

>> sol = solve(eq1,eq2,[a,b]);

>> real(sol.a)
ans =
8*2^(1/2) + 36/5

>> imag(sol.a)
ans =
4*2^(1/2) - 72/5

b will be similar. The symbolic toolbox chooses to group the sqrt(2) stuff together, but I don't see the problem either way. If I had to guess, look at the expression:

sol.a
ans =
2^(1/2)*(8 + 4i) + 36/5 - 72i/5

Here, we have 8+4i as ONE number. A complex number, yet only one number. Likewise, (36/5 - 72i/5) may be thought of as only one number, not two numbers, just one complex number. So the form returned is actually simpler than what you want to see.

[Aleem Andrew]

Thank you for your answer.