Calculator Inputs
Example Data Table
| Series Type | Input | Terms | Expected Sum | Note |
|---|---|---|---|---|
| General Finite | 2+3i, -1+4i, 5-2i | 3 | 6+5i | Direct addition of listed terms. |
| Arithmetic | a₁ = 1+2i, d = 1-i | 5 | 15+0i | Uses arithmetic series sum formula. |
| Geometric | a₁ = 2+i, r = 0.5 | 4 | 3.75+1.875i | Finite geometric sum with real ratio. |
Formula Used
General finite series: Sn = z1 + z2 + ... + zn
Arithmetic complex series: Sn = n/2 × [2a + (n − 1)d]
Geometric finite series: Sn = a(1 − rn) / (1 − r), for r ≠ 1
Geometric infinite series: S∞ = a / (1 − r), valid when |r| < 1
Polar values: |z| = √(x² + y²) and arg(z) = atan2(y, x)
Each complex number is treated as x + yi. The calculator adds or transforms the real and imaginary parts together, then reports rectangular form, magnitude, phase, and a detailed term-by-term table.
How to Use This Calculator
- Select the desired series type.
- Enter either explicit terms or the series parameters.
- Choose whether the phase should appear in degrees or radians.
- Click Submit to place results above the form.
- Review the calculated sum, convergence notes, and generated term table.
- Use the CSV or PDF buttons to export the visible results.