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### The Maxima on-line user's manual

Algebra Calculator

#### 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) ```

### Related Examples

##### conjugate-exp-phi-sin-trigsimp

ph1(z,t):= exp(-%i*(E...

ph2(z,t):= exp(-%i*(E...

phi(z,t):= A*ph1(z,t)...

Calculate

##### conjugate-invert-matrix-sqrt-true

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

w_: conjugate(w);

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

Calculate

##### conjugate-transpose

transpose(conjugate([...

Calculate

##### conjugate-expand

(1/(c*z + d)^4 - 1/(c...

Calculate

##### conjugate-imagpart-plot2d-realpart-sqrt

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

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

plot2d([[discrete, p1...

Calculate

##### conjugate-matrix-simp-sqrt-true

simp:true;

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

w_: conjugate(w);

Calculate

##### conjugate-eval-invert-load-matrix-sqrt

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

w_: conjugate(w);

BaseX:matrix([1/sqrt(...

Calculate

##### conjugate-matrix-ratsimp-sqrt-transpose

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

wbar:conjugate(w);

[1,w,w^2];

Calculate

##### conjugate-plot2d

f(z) := %i*conjugate(z);

plot2d([discrete,[[10...

Calculate

##### conjugate

latex(conjugate(x));

Calculate