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The Maxima on-line user's manual

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Polarform

 Function: polarform (<expr>)
     Returns an expression r %e^(%i theta) equivalent to <expr>, such
     that r and theta are purely real.

R1:4990;
R2:680;
R3:200;
R4:2000;
C3:3.3e-9;
C4:22e-9;
C5:220e-12;
ESR:0.0009;
Rout:5/3;
Cout:22e-6;
L:18e-6;
fz1: 1/(2*%pi*C3*(R1+R3));
fz2: 1/(2*%pi*R4*C4);
fp0: 0;
fp1: 1/(2*%pi*R3*C3);
fp2: 1/(2*%pi*R4*C4*C5/(C4+C5));
Q : sqrt(Rout*L*Cout*(Rout+ESR))/(L+Cout*Rout*ESR);
fLC : 1/(2*%pi*sqrt(L*Cout)*sqrt(1+ESR/Rout));
glc(s):= (1+s/(2*%pi/(2*%pi*ESR*Cout)))/(1+s/(2*%pi*Q*fLC)+(s/(2*%pi*fLC))^2);
float(Q);
float(sqrt(1));
float(glc(5));
gtypeIII(s) := 10^(150/20)*(s-fz1*2*%pi)*(s-fz2*2*%pi)/( (s-fp0*2*%pi) * (s-fp1*2*%pi) * (s-fp2*2*%pi) );
gloop(s):= 18 * glc(s) * gtypeIII(s);
float(rectform(gloop(%i*2*%pi*10^3.8)));
float(polarform(gloop(%i*2*%pi*10^3.8)));
float(carg(gloop(%i*2*%pi*10^3.8)));
atan(float(imagpart(gloop(%i*2*%pi*10^3.8)))/float(realpart(gloop(%i*2*%pi*10^3.8))))/%pi*180;
myCArg(z) := float(atan(float(imagpart(z))/float(realpart(z))))-(signum(realpart(z))/2-.5)*%pi;
float(myCArg(gloop(%i*2*%pi*10^3.8))/%pi*180);
float(myCArg(gloop(%i*2*%pi*10^4))/%pi*180);
float(myCArg(gloop(%i*2*%pi*10^5.8))/%pi*180);
float(myCArg(gloop(%i*2*%pi*10^6))/%pi*180);
plot2d(20*log(cabs(gloop(%i*2*%pi*10^f)))/log(10), [f,-1,6]);
plot2d(float(myCArg(expand(gloop(%i*2*%pi*10^f)))/%pi*180), [f,-1,6]);

(%o1)                                true
(%i2) 

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polarform-solve

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z: 2+sqrt(5)*%i;

polarform(1/z);

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polarform

z: -5+%i*5;

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polarform

polarform(%i);

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polarform

z:5-4*%i;

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