square root of a complex expression

[elvis0206]

suppose z=(a+jb)^1/2

how can we simply it to z=k1+jk2 ????
hope can help such complex problem.

 

[_Eduardo_]

Let p = sqrt(a^2 + b^2)

Then:
k1 = sqrt((p+a)/2)
k2 = sign(b)*sqrt((p-a)/2)

zroot = +/- (k1+i k2)

 

[Prof78]

If you are doing complex algebra you should already be aware of De'Moivre's theorem. For z=(x+jy) then:

z=Re^jθ = R(Cosθ+jSinθ)
with x=RCosθ, y=RSinθ, R=√(x^2+y^2), θ=ArcTan(y/x) and

z^n=R^n .e^jnθ

which holds for integer or fractional n e.g in your case ½. You should now be able to find the rationalized expression you want.