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conjugate

simplify((a+s)*(b+s)*...

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conjugate

(h.s).conjugate(h);

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conjugate-invert-matrix-sqrt-true

w: -1/2 + sqrt(-3)/2;

w_: conjugate(w);

BaseX:matrix([1, w], ...

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conjugate-cos-expand-matrix-sin-sqrt-transpose

a:matrix([1,0],[0,1]);

b:matrix([o,-%i],[%i,...

m:matrix([a,-b],[a,b]);

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conjugate-matrix-ratsimp-sqrt-transpose

w:-1/2+%i*sqrt(3)/2;

wbar:conjugate(w);

[1,w,w^2];

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conjugate

U : 100;

w : 100;

R1 : 1000;

Calculate

conjugate-exp-integrate

f(x):= exp(%i*n*x);

g(x):= exp(-%i*m*x);

integrate(conjugate(f...

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conjugate-ev-invert-load-matrix-simp-sqrt-true

w: -1/2 + sqrt(-3)/2;

w_: conjugate(w);

BaseX:matrix([1/2, w/...

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conjugate-imagpart-plot2d-realpart
plot2d([[discrete, p1], [discrete,p2], [discrete,p3], x], [x,-4,3],[style, points, points, points, lines],  [legend, "2 and f(2)", "-i and f(-i)" ,"3-i and f(3-i)", "x=y"],[xlabel, "Re(z)"], [ylabel, "Im(z)"]);

f(z) := %i * conjugat...

p1: [[2,0],[realpart(...

p2: [[0,-1],[realpart...

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conjugate-eigenvalues-matrix-sqrt

i:sqrt(-1) ;

m:matrix([0,a,0,i*gp]...

A:eigenvalues(m) ;

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conjugate

Run Example
(%i1)? conjugate ;

 -- Function: conjugate (<x>)
     Returns the complex conjugate of <x>.

          (%i1) declare ([aa, bb], real, cc, complex, ii, imaginary);

          (%o1)                         done
          (%i2) conjugate (aa + bb*%i);

          (%o2)                      aa - %i bb
          (%i3) conjugate (cc);

          (%o3)                     conjugate(cc)
          (%i4) conjugate (ii);

          (%o4)                         - ii
          (%i5) conjugate (xx + yy);

          (%o5)             conjugate(yy) + conjugate(xx)


(%o1)                                true
(%i2) 
Run Example
conjugate(2+i4);
(%o1)                               i4 + 2
(%i2) 
Run Example
declare(r,real);
(%o1)                                done
(%i2) declare(t,real);
(%o2)                                done
(%i3) a:K1*r*exp(%i*t)+K2*r**2*exp(%i*2*t)+K3*r**3*exp(%i*3*t);
                  3   3 %i t       2   2 %i t          %i t
(%o3)            r  %e       K3 + r  %e       K2 + r %e     K1
(%i4) Bt:diff(a,r);
                   2   3 %i t            2 %i t        %i t
(%o4)           3 r  %e       K3 + 2 r %e       K2 + %e     K1
(%i5) Br:diff(a,t)/r;
                3   3 %i t            2   2 %i t             %i t
          3 %i r  %e       K3 + 2 %i r  %e       K2 + %i r %e     K1
(%o5)     ----------------------------------------------------------
                                      r
(%i6) factor(Bt*conjugate(Bt)+Br*conjugate(Br));
          - 2 %i t     2            %i t        2 %i t
(%o6) 2 %e         (3 r  K3 + 2 r %e     K2 + %e       K1)
                                            2   2 %i t            %i t
                                        (3 r  %e       K3 + 2 r %e     K2 + K1)
(%i7) 
[abs,conjugate,expand,solve] [abs,conjugate,expand] [beta,conjugate,realpart] [complex,conjugate,declare,matrix,transpose] [complex,conjugate,declare,ratsimp,realpart] [complex,conjugate,declare,ratsimp] [complex,conjugate,declare] [conjugate,cos,eigenvectors,factor,matrix,sin,transpose] [conjugate,cos,expand,matrix,sin,sqrt,transpose] [conjugate,cos,factor,matrix,sin,sqrt,transpose] [conjugate,cos,factor,matrix,sin,sqrt] [conjugate,cos,matrix,sin,sqrt,transpose] [conjugate,cos,matrix,sin,sqrt] [conjugate,cos,matrix,sin] [conjugate,declare,diff,exp] [conjugate,declare,imagpart] [conjugate,declare,realpart] [conjugate,declare] [conjugate,diff,exp,linsolve] [conjugate,diff,phi,sqrt] [conjugate,diff] [conjugate,eigenvalues,matrix,sqrt] [conjugate,ev,invert,load,matrix,simp,sqrt,true] [conjugate,ev,invert,load,matrix,sqrt] [conjugate,ev,invert,matrix,sqrt] [conjugate,eval,invert,load,matrix,sqrt] [conjugate,exp,integrate] [conjugate,exp,phi,sin,sqrt] [conjugate,exp,phi,sin,trigreduce,trigsimp] [conjugate,exp,phi,sin] [conjugate,expand,solve,subst] [conjugate,expand] [conjugate,imagpart,plot2d,realpart] [conjugate,integrate,phi] [conjugate,integrate] [conjugate,invert,load,matrix,sqrt,true] [conjugate,invert,matrix,simp,sqrt,true] [conjugate,invert,matrix,sqrt,true] [conjugate,invert,matrix,sqrt] [conjugate,load,matrix,ratsimp,sqrt,transpose] [conjugate,matrix,ratsimp,sqrt,transpose] [conjugate,matrix,simp,sqrt,true] [conjugate,matrix,sqrt,transpose] [conjugate,matrix,sqrt] [conjugate,matrix,transpose] [conjugate,numer] [conjugate,plot2d] [conjugate,sqrt] [conjugate,transpose] [conjugate]

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