Certified calculator · Version 1

Complex Number Calculator

Perform deterministic arithmetic on two complex numbers and inspect rectangular result, magnitude and argument.

First real (a)First imaginary (b)Second real (c)Second imaginary (d)

Operation

Result4 + 6i

Real component4

Imaginary component6

Magnitude7.21

Argument (radians)0.98

CalcuMint Pro

Advanced Analysis

Compare plans

Advanced chartsExplore the result across time and assumptions.

Scenario comparisonCompare multiple assumptions side by side.

Sensitivity analysisSee which assumptions change the outcome most.

Goal SolverSolve backwards from the outcome you want.

Result methodology

The certified complex-arithmetic engine performs the selected operation first, then derives magnitude and argument from the same deterministic result.

Solution steps

Operation: add
Result = 4 + 6i
|z| = 7.211102550927979

How this calculator works

The engine applies standard complex arithmetic identities to (a+bi) and (c+di), then derives magnitude and argument from the resulting real and imaginary components.

Formula

(a+bi) ⊕ (c+di)

Applies deterministic complex addition, subtraction, multiplication or division and reports rectangular and polar properties.

Worked example

(1+2i)+(3+4i) is a verified test case used by the calculation engine.

Assumptions and limitations

Inputs are finite real components.
Division by 0+0i is not allowed.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint.

CalcuMint deterministic complex-arithmetic engine — Standard complex-number arithmetic identities.

Frequently asked questions

Which operations are supported?

Addition, subtraction, multiplication and division.

Does it show polar information?

Yes. The result includes magnitude and argument in radians.