The principal square root of a complex number a + jb (where j = 1) is given by p a + jb = s a 2 + b 2 + a 2 + j sign(b) s a 2 + b 2 a 2 . Here sign(b) is defined as 1 if b 0 and as 1 if b < 0. 1. We used the MATLAB code x = sqrt((sqrt(a^2 + b^2) + a) / 2); y = sign(b) * sqrt((sqrt(a^2 + b^2) - a) / 2); to compute the real and imaginary parts of the square roots of the two complex numbers a + jb = 106 106 + j2, a + jb = 106 106 + j2, and obtained the following results. a + jb Exact square root x y 106 106 + j2 103 + j103 1.000000000000000e+03 1.000003807239438e-03 106 106 + j2 103 + j103 1.000003807239438e-03 1.000000000000000e+03 In the first result, the computed real part x is very accurate but not the imaginary part y. In the second result, it is the opposite. Explain these errors