Numbers
Calculadora de números complejos
Used by developers, writers, and creators worldwide.
A complex number calculator takes the real and imaginary parts of a complex number and returns its key properties. Enter the real part and the imaginary part and it gives the number in standard a plus bi form, its modulus or absolute value, its argument or angle in both degrees and radians, the complex conjugate, and the equivalent polar form. Complex numbers extend the reals to include the square root of negative one and are indispensable in electrical engineering, signal processing, control theory, and physics, where they capture both magnitude and phase. Students use the tool to check homework on modulus and argument, engineers to convert between rectangular and polar representations, and anyone learning the subject to see how the parts fit together. The argument uses a quadrant-aware calculation, so it is correct wherever the number sits. Use it to analyse a number or switch between forms.
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How to use
- Choose your options above
- Click Generate
- Copy your result
Detailed instructions
- Enter the real part of the number.
- Enter the imaginary part of the number.
- Click Generate to compute its properties.
- Read the modulus, argument, conjugate, and polar form.
Use Cases
- •Finding the modulus and argument of a complex number
- •Converting between rectangular and polar form
- •Checking complex number homework
- •Computing the conjugate for division problems
- •Visualising where a number sits in the complex plane
Tips
- →Modulus is the distance from the origin in the plane.
- →The conjugate flips only the sign of the imaginary part.
- →Polar form pairs a magnitude with an angle.
- →A number times its conjugate equals the modulus squared.
FAQ
what are the modulus and argument
The modulus is the distance from the origin to the number in the complex plane, like a magnitude. The argument is the angle that line makes with the positive real axis, giving the number a length and a direction.
what is the complex conjugate
The conjugate keeps the real part and flips the sign of the imaginary part. It is central to dividing complex numbers and computing magnitudes, since a number times its conjugate is the square of the modulus.
how is the argument kept correct in every quadrant
The tool uses a quadrant-aware angle calculation rather than a plain inverse tangent, so the argument is right whether the number lies in the upper, lower, left, or right part of the complex plane.
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