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Maple worksheets on complex numbers |
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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
