Simplifying solution to algebraic system of equations

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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

Accepted Answer

John D'Errico
John D'Errico on 21 Apr 2020
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:
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.

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