Complex Number Calculator — GetCalcMaster

Complex arithmetic with verification

The Complex Number Calculator helps you work in rectangular form (a + bi) and polar form (r∠θ). It supports common operations (conjugate, magnitude, argument, powers/roots) so you can verify algebra and build intuition for signals, control, and electromagnetics.

Open the tool

• Complex Calculator — rectangular & polar workflows
• Scientific Calculator — real-only checks and constants

Example inputs to test

• (3+4i)*(1-2i) → 11 - 2i
• sqrt(-1) → i (principal root)
• conj(3+4i) → 3 - 4i
• abs(3+4i) → 5
• arg(1+i) → π/4 (≈ 0.785398… radians)
• cis(45) in DEG mode → 0.7071 + 0.7071i

Rectangular ↔ polar workflow

• Rectangular → polar: compute r = abs(z) and θ = arg(z).
• Polar → rectangular: compute r * cis(θ) and compare with a+bi.

Worked guides: Rectangular → polar and Polar → rectangular.

Common pitfalls

• Angle mode: functions that interpret angles (cis, sin, cos) depend on DEG/RAD mode.
• Branch cuts: complex sqrt, ln, and fractional powers use principal values. If you expect a different branch, compare against polar form and note the angle.
• Formatting: switch between rectangular/polar output to confirm magnitude/phase agree.

Verification habit

A reliable manual check is: compute abs(z) and arg(z), then reconstruct using abs(z) * cis(arg(z)). The reconstructed value should match the original (up to rounding).

FAQ