Index | math | Lists | strings | complex | matrix | poly |
hexa/bin | date/time | progs | conversion | files | apn |
(2;1)
is 2+i(2@1)
will be interpreted as (2 @:1)
(1;2)
or as polar (2 @:1.5)
.
Cartesian mode is (x;y) |
z = x + i y |
Polar mode is (ρ @:θ) ρ stand for rho, the magnitude (module) and θ is the angle. |
z = ρ * ei θ |
(1;1)
<>(x;y) gives : (1.414213 @:0.785398)
or (sqr(2) @:pi/4)
if you use the rationalize mode : - recomended. function | usage | example |
C->XY | Gives the two cartesian values of a complex. | (1;2) gives 1 and 2 |
C->R@ | Gives the two polar values of a complex. | (1;1) gives 1.4142135... and 0.785398... |
XY->C | Perform the reversal of C->XY : build a complex from two numbers | the stack has :
5 6we execute function XY->C it gives : (5;6) |
conj | compute the conjugate of a complex | (1;2) gives (1;-2) polar : (3 @:1) gives (3 @:-1) |
ABS | compute the Magnitude of a complex | (1;2) gives 2.23606 |
-4
sqr you will get a (nan)
: not-a-number ---> an error.(-4;0)
sqr, you will get : { (0;2) (0;-2) }
this is the only exact mathematical result of sqr(-4) !function extended | for information, in REAL mode | beavior in COMPLEX |
sqr | just give the first root (and only in positive), as all other dummy calculator-4 gives (nan) 4 gives 2 (not suffisant, -2 is missing) |
gives all two roots, sqr function is defined for positives and negatives(-4;0) gives { (0;2) (0;-2) } (4;0) gives { (2;0) (-2;0) } correct! |
ln | this function is defined for >= 0-1 gives (nan) |
extended to negatives(-1;0) gives (0;3.1415...) |
x^y where y=1/n |
gives only the first of nth roots2 0.5 gives 1.41421.. |
gives all the nth roots(2;0) 0.5 gives {(1.41..;0)(-1.41..;0)} if n=5, it gives you a list of 5 roots. |
functions | behavior | notes/example |
Trigonometrics SIN/COS/TAN |
basic trigonometrics are defined. please note that ASIN, ACOS and ATAN are not yet defined. | (1;1) COS gives (1.2984..;0.6349..) |
e | exponential of complex works. works for any basis : 10^x |
(1;1) e gives (1.468..;2.287..) |
ln | logarithms of complex works also for any basis : log |
(1;1) ln (0.346..;0.785...) |
1/x | compute 1/x | (1;1) 1/x gives (0.5;-0.5) |
x^y | This is a very specific function. x and y can be complex. see the next table for details |
See detailed examples on next table |
Sqr | Sqr is exactly the same as x^(1/2), see x^y function (where y=0.5) |
See x^y on the table that follow for details.(1;1) Sqr gives { (1.098..;0.455..) (-1.098..;-0.455..) } there are two roots. |
x | y | result |
real2 |
real2 |
compute 22, it gives 4 |
complex(2;1) |
compute 2(2+i) : (3.0769...;2.5558...) |
|
complex(2;1) |
integer3 |
compute (2+i)3 : (2;11) |
1/integer0.3333333333 |
compute all the n root{(1.29;0.20) (-0.82;1.01) (-0.47;-1.21)} |
|
other real1.2556 |
(2;1)^1.2256 gives (2,25983..;1,44289..) |
|
complex(2;2) |
compute (2;1)(2;2) = (2+i)^(2+2i) : (-1.62...;1.12...) |
(2;0)
5
1/x x^y gives :{(1.148698354;0) (0.3549673131;1.092477055) (-0.9293164906;0.6751879523) (-0.929316490;-0.6751879523) (0.3549673131;-1.092477055) }
This is the list of the 5 roots.(`12233`;`55566`)
, only basic operations are supported yet...