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

Algebra Calculator

#### Complex

6.2 Complex===========

A complex expression is specified in Maxima by adding the real part ofthe expression to `%i` times the imaginary part. Thus the roots of theequation `x^2 - 4*x + 13 = 0` are `2 + 3*%i` and `2 - 3*%i`. Note thatsimplification of products of complex expressions can be effected byexpanding the product. Simplification of quotients, roots, and otherfunctions of complex expressions can usually be accomplished by usingthe `realpart`, `imagpart`, `rectform`, `polarform`, `abs`, `carg`functions.

There are also some inexact matches for `complex`. Try `?? complex` to see them.

```(%o1)                                true
(%i2) ```

### Related Examples

##### complex-domain-imagpart-makelist-plot2d-realpart

domain:complex;

ImList:makelist(imagp...

ReList:makelist(realp...

Calculate

##### complex-residue-sqrt

residue(1/(s-c),s,c);

c=complex;

(sqrt(c))^3;

Calculate

##### complex-conjugate-declare

declare ([h1, h2, h3,...

conjugate(h1)*h1;

Calculate

##### complex-define-determinant-diff-domain-factor-hessian

domain:complex;

define(F(x,y,z),(z+y-...

diff(diff(diff(F(x,y,...

Calculate

##### complex-diff-domain-sqrt

domain:complex;

F(x,y,z):=(z+(3/2)*y+...

YY(x,y,z)=diff(diff(F...

Calculate

##### complex-define-domain-hessian

domain:complex;

define(F(x,y,z),(z+y+...

hessian(F(x,y,z),[x,y...

Calculate

##### complex-declare-depends-diff

declare(u, complex);

depends(u, [z, t]);

diff(u, z);

Calculate

##### complex-define-domain-factor-hessian

domain:complex;

define(f(x,y,z),(z+y+...

define(H(x,y,z),hessi...

Calculate

##### complex-define-determinant-domain-factor-hessian

domain:complex;

define(F(x,y,z),x*(z+...

define(H(x,y,z),deter...

Calculate

##### complex-conjugate-declare-ratsimp

declare (Za, complex);

eq1: (Za+%i*w*L)*(1/(...

ratsimp(eq1);

Calculate