Complex Equation Solver

Solve linear, quadratic, polynomial, and exponential equations with complex solutions

Equation Type

Coefficients

a (x² coefficient)

b (x coefficient)

c (constant term)

Solution Formulas

Linear Equation

ax + b = 0

x = -b/a

Quadratic Equation

ax² + bx + c = 0

x = (-b ± √(b²-4ac)) / 2a

Exponential Equation

ae^x + b = 0

x = ln(-b/a) if -b/a > 0

|z| = √(a² + b²)

Applications

Engineering

Circuit analysis (complex impedance)
Control systems
Signal processing
Vibration analysis

Physics

Quantum mechanics
Wave equations
Electromagnetic fields
Fluid dynamics

Complex Solutions

Complex numbers extend the real number system to include solutions to equations that have no real roots. They are essential in many areas of science and engineering, representing quantities with both magnitude and direction, such as electrical impedance and quantum states.