Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronic Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

square root of a complex expression

Status
Not open for further replies.

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.
 

_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
2,842
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

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:

Status
Not open for further replies.

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Top