Complex Numbers Visual Tools

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Explore Interactive Complex Number Tools

Master complex numbers through hands-on visualization on the Argand plane.

💡Tip: Click any tool below to see its description and start exploring.

10Tools

4Categories

100%Free

3 tools

Arithmetic

Complex Addition & Subtraction Visualizer

Add and subtract complex numbers geometrically. Drag two points and watch the parallelogram rule for addition and the difference vector for subtraction update instantly, with step-by-step component breakdowns and the triangle inequality verified in real time.

Complex Division Visualizer

Visualize complex division geometrically — moduli divide, angles subtract. See the conjugate multiplication method step by step alongside the polar interpretation, with a zoom inset for small quotients.

Complex Multiplication Visualizer

See complex multiplication as rotation and scaling. Drag two points and watch the product vector update — moduli multiply, angles add. Follow both the FOIL algebraic method and the geometric polar method side by side.

2 tools

Modulus & Geometry

Complex Conjugate and Modulus Visualizer

Drag a point on the Argand plane to see z and its conjugate z̄ mirrored across the real axis. Watch the modulus circle, right triangle decomposition, and the proof that z · z̄ = |z|² update in real time.

Complex Distance & Midpoint Calculator

Compute and visualize the distance |z₁ − z₂| and midpoint between two complex numbers. Drag two points to see the right triangle, step-by-step calculations, and a circle of radius equal to the distance centered at z₁.

2 tools

Plane & Representation

Complex Number Explorer

Visualize complex numbers on an interactive Argand plane. Drag points or enter coordinates to see real parts, imaginary parts, modulus, and conjugates. Watch the right triangle form as you explore different quadrants with real-time calculations and explanations.

Polar-Rectangular Complex Number Converter

Convert between rectangular form a + bi and polar form r·eⁱᶿ interactively. Drag a point on the Argand plane to see modulus, argument, and live conversion formulas update in real time, with the right triangle bridging both representations.

3 tools

Powers & Exponential

De Moivre's Theorem Visual Calculator

Raise any complex number to any integer power and watch the result animate on the plane. See modulus scale and angle multiply, follow the step-by-step polar calculation, and trace intermediate powers as a spiral trail.

Euler's Formula Explorer

Explore eⁱᶿ = cos θ + i sin θ on an interactive unit circle. Drag the angle or use the slider, see the right triangle projections, hit landmark angles like Euler's identity eⁱᵖ = −1, and scale with r for the full polar form.

Powers of i Calculator

Calculate any power of i instantly. See the 4-step cycle in a dynamic diagram, follow the division-by-4 method step by step, and look up results from i⁰ to i¹⁰⁰ in the reference table.