May 18, 2011 #1 E elvis0206 Junior Member level 1 Joined Oct 21, 2010 Messages 15 Helped 0 Reputation 0 Reaction score 0 Trophy points 1,281 Activity points 1,400 suppose z=(a+jb)^1/2 how can we simply it to z=k1+jk2 ???? hope can help such complex problem.
May 18, 2011 #2 _Eduardo_ Full Member level 5 Joined Aug 31, 2009 Messages 295 Helped 118 Reputation 238 Reaction score 103 Trophy points 1,323 Location Argentina Activity points 2,909 Let p = sqrt(a^2 + b^2) Then: k1 = sqrt((p+a)/2) k2 = sign(b)*sqrt((p-a)/2) zroot = +/- (k1+i k2)
May 21, 2011 #3 P Prof78 Junior Member level 1 Joined Jan 2, 2011 Messages 16 Helped 6 Reputation 12 Reaction score 5 Trophy points 1,283 Location Manchester UK Activity points 1,528 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. Last edited: May 21, 2011
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.