Maple worksheets on complex numbers |

Vectors, matrices and complex numbers:

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

An Introduction to complex numbers- complex.mws

- Solving quadratic equations and the imaginary unit.
- Argand diagrams, the modulus and conjugate of a complex number.
- Arithmetic operations on complex numbers.
- A note on programming complex arithmetic.

The polar form for complex numbers- polar.mws

- The argument of a complex number.
- The polar form of a complex number.
- Multiplication and division of complex numbers in polar form.

Plotting complex solutions of equations- plotcomplex.mws

- Plotting the complex solutions of an equation.
- A procedure for plotting lists of complex numbers in the complex plane:
plotcomplex.plotcomplex: examples.

Graphing functions of a complex variable- conformalplot.mws

- A procedure for plotting functions of a complex variable:
conformalplot.conformalplot: examples.

Functions of a complex variable defined by power series, the exponential function and Euler's formula- exp_cmplx.mws

- Convergent geometric series of complex numbers - introductory example.
- Convergent geometric series of complex numbers - theory.
- Power series of complex numbers.
- The exponential function w = exp(z).
- The index law exp(z)*exp(w)=exp(z+w).
- Euler's formula
- Euler's formula and
convert(..,exp).- The graph of w = exp(z).

Linear functions of a complex variable- lin_cmplx.mws

- Rotation, Translation, dilation and rotation.
- A general linear complex function.
- The transformation corresponding to multiplication by a complex number.

Trigonometrical and hyperbolic functions of a complex variable- trig_cmplx.mws

- The sine and cosine functions of a complex variable.
- The addition formulas
- The graph of w = sin(z).
- The graph of w = cos(z).
- The hyperbolic sine and cosine functions of a complex variable.

The logarithm function of a complex variable- log_cmplx.mws

- The natural logarithm function of a complex variable.
- The graph of w = ln(z).

The derivative of a function of a complex variable- deriv_cmplx.mws

- Definition of the derivative of a complex function.
- Linear approximation for w = exp(z).
- Linear approximation for w = sqrt(z).
- Linear approximation for w = sin(z^2).

The derivative of a function of a complex variable II- deriv_cmplx2.mws

- An investigation of the function w = z + 1/z.

An elementary treatment of Euler's formula- euler_form.mws

- The series expansion of exp(x).
- Calculation of e using the series.
- Series expansions of sin(x) and cos(x).
- The exponential function of a complex variable.
- The exponential form of a general complex number.
- Trigonometric and hyperbolic functions of a complex variable.

Graphical procedures for complex numbers-complex.zip