| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 1100.1 | Some helpful identities | POOL::HALLYB | The Smart Money was on Goliath | Fri Jul 14 1989 16:06 | 6 |
| a+bi (a+bi)Ln X
X = e
iy
e = cos(y) + i�sin(y)
|
| 1100.2 | | RDVAX::NG | | Fri Jul 14 1989 20:58 | 7 |
| You will also need this:
Ln z = ln |z| + i*arg(z); z = x+iy
where the second 'ln' is the natural logarithm for the real number,
|z| = (x^2+y^2)^0.5 and 'arg' stands for the angle of the complex
number z.
|
| 1100.3 | | AITG::DERAMO | Daniel V. {AITG,ZFC}:: D'Eramo | Fri Jul 14 1989 22:33 | 13 |
| Write a + bi as re^(it) [that's "t" for "theta"]
where r^2 = x^2 + y^2 and e^(it) = cos t + i sin t, and
the "principal value" (or is it "principle value"?) of t
is used.
Then (a + bi)^(c + di) = (re^(it))^(c + di)
= (e^(ln r + it)) ^ (c + di)
= e^((ln r + it)(c + di))
= e^( c ln r - dt + (d ln r + ct)i )
= (e^x)(cos y + i sin y) where x = c ln r - dt
y = d ln r + ct
Dan
|
| 1100.4 | with other functions too | ANT::JANZEN | cf. ANT::CIRCUITS,ANT::UWAVES | Mon Jul 17 1989 12:35 | 3 |
| This is all defined in my complex arithmetic package for Ada in the
Ada toolshed conference.
Tom
|
| 1100.5 | Thanks | DRUMS::FEHSKENS | | Wed Jul 19 1989 11:28 | 7 |
| This all looks familiar, I just wasn't sure I could do exponentials
the same way with complex numbers as reals.
Thanks for the confirmation.
len.
|