Table 4 Complex factorials of some imaginary numbers
From: Factorials of real negative and imaginary numbers - A new perspective
z | Complex factorial of ( iz ) | |||
|---|---|---|---|---|
Real | Imaginary | Modulus | Im/Re | |
0 | 1 | 0 | 1 | 0 |
0.25 | 0.837 | 0.346i | 0.906 | 2.414 |
0.5 | 0.626 | 0.626i | 0.886 | 1 |
0.75 | 0.351 | 0.849i | 0.919 | 2.414 |
1 | 0 | i | 1 | Comp Inf |
1.25 | -0.433 | 1.046i | 1.133 | -0.414 |
1.5 | -0.939 | 0.939i | 1.329 | -1 |
1.75 | -1.485 | 0.615i | 1.608 | -2.414 |
2 | -2 | 0 | 2 | 0 |
2.25 | -2.355 | -0.975i | 2.549 | 2.414 |
2.5 | -2.349 | -2.349i | 3.323 | 1 |
2.75 | -1.692 | -4.086i | 4.422 | 0.414 |
3 | 0 | -6i | 6 | Comp Inf |
z | Complex factorial of (- iz ) | |||
0 | 1 | 0 | 1 | 0 |
0.25 | 0.837 | -0.346i | 0.906 | -0.414 |
0.5 | 0.626 | -0.626i | 0.886 | -1 |
0.75 | 0.351 | -0.849i | 0.919 | -2.414 |
1 | 0 | -i | 1 | Comp Inf |
1.25 | -0.433 | -1.046i | 1.133 | 2.414 |
1.5 | -0.939 | -0.939i | 1.329 | 1 |
1.75 | -1.485 | -0.615i | 1.608 | 0.414 |
2 | -2 | 0 | 2 | 0 |
2.25 | -2.355 | 0.975i | 2.549 | -2.414 |
2.5 | -2.349 | 2.349i | 3.323 | -1 |
2.75 | -1.692 | 4.086i | 4.422 | -0.414 |
3 | 0 | 6i | 6 | Comp Inf |