Complex arithmetic, modulus, polar form, Euler's formula, and de Moivre's theorem.
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Add, subtract, multiply, and divide complex numbers in rectangular form.
Find the modulus |z| = √(a² + b²) of any complex number.
Convert polar form r∠θ to rectangular form a + bi.
Evaluate e^(iθ) = cos θ + i sin θ for any angle θ.
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Add, subtract, multiply, and divide complex numbers in rectangular form.
Find the modulus |z| = √(a² + b²) of any complex number.
Find the argument arg(z) = atan2(b, a) of a complex number.
Compute the conjugate z̄ = a − bi of any complex number.
Convert polar form r∠θ to rectangular form a + bi.
Convert rectangular form a + bi to polar form r∠θ.
Evaluate e^(iθ) = cos θ + i sin θ for any angle θ.
Calculate e^z for any complex number z = a + bi.
Compute the square roots of any complex number.
Raise a complex number z to a complex power n.
Apply z^n = r^n(cos nθ + i sin nθ) using De Moivre's Theorem.
Divide two complex numbers z₁/z₂ with detailed steps.
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Our complex numbers calculators provide accurate, instant results for students, teachers, and professionals. Each calculator uses mathematically verified formulas and handles edge cases like invalid inputs, division by zero, and overflow conditions.
Whether you need to solve equations, compute integrals, find prime factors, or convert between number bases, our complex numbers tools deliver reliable results with step-by-step explanations to help you understand the underlying mathematics.
