### Related

demoivre;

%e^(%i*w);

expr:%e^(%i*w);

Calculate

##### demoivre-diff-exp-linsolve-ode2-sin

ode2('diff(y,t,2)+0*'...

linsolve([21*b+a=0,b-...

demoivre(%i*exp(-%i*x));

Calculate

f:demoivre(exp(%i*t));

Calculate

##### demoivre-exp-polarform

z : 4 *exp(%i *5);

polarform(z);

demoivre(polar);

Calculate

##### demoivre

z1: 2+3*%i;

z2 : -1 -5*%i;

demoivre(z1 / z2);

Calculate

##### demoivre-expand

demoivre(expand(((1-a...

Calculate

##### demoivre

eq1:(8*3^(x+1)+3*x)/(...

demoivre(eq1);

Calculate

##### demoivre-exp-polarform

z : 4 *exp(%i *5);

polarform(z);

demoivre(z);

Calculate

##### demoivre-diff-exp-linsolve-ode2-sin

ode2('diff(y,t,2)+2*'...

linsolve([21*b+a=0,b-...

demoivre(%i*exp(-%i*x));

Calculate

##### demoivre

demoivre(%e^(%i*w));

Calculate

### demoivre

Run Example
```(%i1)eq: diff(r(t),t,2)-C*r(t)=0;
2
d
(%o1)                       --- (r(t)) - r(t) C = 0
2
dt
(%i2) eq2:diff(r(t), t, 2)=0;
2
d
(%o2)                           --- (r(t)) = 0
2
dt
(%i3) assume(C<
0);
(%o3)                               [C < 0]
(%i4) ode2(eq, r(t), t);
(%o4)         r(t) = %i %k1 sinh(t sqrt(C)) + %k2 cosh(t sqrt(C))
(%i5) forget(facts());
(%o5)                              [[C < 0]]
(%i6) assume(C>
0);
(%o6)                               [C > 0]
(%i7) ode2(eq, r(t), t),demoivre;
t sqrt(C)         - t sqrt(C)
(%o7)             r(t) = %k1 %e          + %k2 %e
(%i8) ode2(eq2, r(t), t);
(%o8)                         r(t) = %k2 t + %k1
(%i9) ```
Run Example
```r:solve(x+1/x, x);
(%o1)                         [x = - %i, x = %i]
(%i2) x:r[1];
(%o2)                              x = - %i
(%i3) demoivre(expand((x+1)^5 + 1/(x+1)^5));
1                     5      4       3       2
(%o3) ----------------------------------- + x  + 5 x  + 10 x  + 10 x  + 5 x
5      4       3       2
x  + 5 x  + 10 x  + 10 x  + 5 x + 1
1
+ 1 = -------- + 4 %i - 4
4 %i - 4
(%i4) ```
Run Example
```demoivre;
(%o1)                                false
(%i2) %e^(%i*w);
%i w
(%o2)                               %e
(%i3) expr:%e^(%i*w);
%i w
(%o3)                               %e
(%i4) demoivre(%e^(%i*w));
(%o4)                         %i sin(w) + cos(w)
(%i5) demoivre(expr);
(%o5)                         %i sin(w) + cos(w)
(%i6) %e^(%i*w),demoivre=true;
(%o6)                         %i sin(w) + cos(w)
(%i7) expr,demoivre=true;
(%o7)                         %i sin(w) + cos(w)
(%i8) demoivre:true;
(%o8)                                true
(%i9) %e^(%i*w);
(%o9)                         %i sin(w) + cos(w)
(%i10) expr;
%i w
(%o10)                              %e
(%i11) ev(expr);
(%o11)                        %i sin(w) + cos(w)
(%i12) ```

### Related Help

Help for Demoivre