doomath Calculator
Complex Numbers & Euler Polar Form
Perform complex arithmetic (addition, subtraction, multiplication, division), compute modulus r, argument θ in degrees and radians, and Euler polar form.
InputsChange a value to recalculate instantly
ResultUpdates as you type
FORMULA & STEPSComplex Numbers & Euler Polar Form — Mathematical Derivation & Steps
2 StepsSequential Calculation Breakdown
1
Add and subtract
Combine real and imaginary components separately.
2
Polar form
Compute modulus and argument with atan2.
λ DooMathWork with this calculation
Local · deterministic · optionalQuick mathNatural-language-style shortcuts for deterministic arithmetic.
Calculator guide
How to use the Complex Numbers & Euler Polar Form
Perform complex arithmetic (addition, subtraction, multiplication, division), compute modulus r, argument θ in degrees and radians, and Euler polar form.
01Set inputsChoose values, units and assumptions.
02Apply the modelz = a + bi = r(cos θ + i sin θ) = r e^{iθ}; r = √(a² + b²); θ = atan2(b, a)
03Read the resultCheck the output against the assumptions before using it.
What this calculator does
Enter real and imaginary components for z₁ and z₂. The calculator evaluates rectangular arithmetic, complex conjugates, and converts to exponential polar coordinates.
Formula & method
z = a + bi = r(cos θ + i sin θ) = r e^{iθ}; r = √(a² + b²); θ = atan2(b, a)
Assumptions & notes
- Euler's formula e^{iθ} = cos θ + i sin θ bridges trigonometry and exponential growth.
- Multiplication in polar form multiplies moduli and adds arguments.
- The complex conjugate reflected across the real axis is a - bi.