May 9, 2004 sfb

The ti-89 and complex numbers.

0a. Entering i = sqrt(-1) on the keyboard. It is 2nd (Yellow key) CATALOG
and not alpha (Purple? key) 9.

0b. Variables are always real unless one of the following are done.
Use underscore as the last character of the variable name, like z_.
Define a complex number x + yi -> z.

1. Sqrt(i) gives sqrt(2)/2 + (sqrt(2)/2)*i

2. cSolve(x^2-i=0,x) gives both square roots. cSolve is F2, A, 1 where
F2 is algebra, A is complex which gives a choice of cSolve, cFactor
and cZeros.

3. The mode button, there are 3 choices for the way to write complex
numbers, real like 1 + sqrt(3)*i but won't display complexs implicitly,
rectangular like 1 + sqrt(3) and polar like exp(i pi/3)*2

Try: Find all 6th of unity by cSolve(x^6=1,x) switch modes from rect to polar
and see the difference.

4. Complex functions include imag (Im), real (Re), abs (|.|), conj
(conjugate), ln, sin, cos, etc.

Other notes. Check out app 11: Visualizing the complex zeros of a cubic
polynomial where f(z) = z^3-z^2+z-1 is plotted via computing
|f(x + y*i)| and doing a 3D plot.

One can plot complex curves using the parameteric plot function of the
real and imaginary parts.