# Solving a system of equations involving complex numbers

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Aleem Andrew on 21 Apr 2020
Commented: Ameer Hamza on 21 Apr 2020
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 it is of the form a+bi where a and b are rounded to a certain number of decimal places? This would ensure that the real and complex parts are each only one number rather than the sum of a radical and a rational numbers.
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
BALAJI KARTHEEK on 21 Apr 2020
The ans is in the form of cells, conversion of cells to arrays will give you the required results..

Ameer Hamza on 21 Apr 2020
Edited: Ameer Hamza on 21 Apr 2020
Try vpasolve()
syms X Y Q t w v a b z c N theta m L g
eq1 = b-a == 10*(cosd(45)+1i*sind(45));
eq2 = 3 == (a-b)/4+a*1i/3 + b/(6*1i)+b/12;
sol = vpasolve([eq1 eq2], [b a]); %[a b c] = [theta' theta'' x'']
Result
>> sol.a
ans =
18.513708498984760390413509793678 - 8.7431457505076198047932451031612i
>> sol.b
ans =
25.584776310850235634421953414726 - 1.6720779386421445607848014821127i
Aleem Andrew on 21 Apr 2020
Ameer Hamza on 21 Apr 2020
I am glad to be of help.