Compute the conjugate and modulus of any complex number z = a + bi step-by-step.
z = a + bi
This calculator helps you compute the complex conjugate and absolute value (modulus) of any complex number z = a + bi instantly. Simply enter the real part a and the imaginary part b, and the calculator displays step-by-step results.
Provide the two components of your complex number:
The calculator instantly updates the results as you type.
The calculator computes:
Results are displayed clearly, with the sign of the imaginary part adjusted automatically.
Ensures reliable calculations:
Ideal for learning and practice:
1. Enter the real part (a) and imaginary part (b) of your complex number.
2. The calculator computes the complex conjugate automatically using: z̄ = a − bi.
3. The absolute value (modulus) is calculated with: |z| = √(a² + b²).
4. Results are displayed instantly in the result section.
5. If either input is missing or invalid, an error message is shown and results are hidden.
This real-time functionality helps students, beginners, and learners explore complex numbers easily.
Suppose you have a complex number:
z = 3 + 4i
The calculator computes:
Conjugate: z̄ = 3 − 4i
Absolute Value: |z| = 5
All results are displayed automatically as you enter any new values for a or b.
Everything you need to know about computing complex conjugates and absolute values accurately and instantly.
This calculator computes the complex conjugate (z̄ = a − bi) and the absolute value |z| = √(a² + b²) of any complex number z = a + bi, showing results instantly and step-by-step.
Yes! It is completely free with no registration, ads, or hidden charges.
You only need to enter the real part (a) and the imaginary part (b) of the complex number. The calculator will automatically compute the conjugate and absolute value.
Yes, both negative and zero values are supported for real and imaginary parts.
If either input is missing or not a number, the calculator will not display a result and may show an error message until valid numbers are entered.
Yes. Use the “Clear All” button to reset the input fields or the “Reload Calculator” button to reload the page completely.
The conjugate is displayed as z̄ = a − bi, and the absolute value is shown as |z| = √(a² + b²), rounded to two decimal places if necessary.
Yes, the calculator is fully responsive and works smoothly on smartphones, tablets, laptops, and desktops.
Students, teachers, or anyone learning complex numbers can use this tool to compute conjugates, absolute values, and better understand complex number operations.
Discover more useful percentage calculators and expert-written blog guides to improve your calculations.
Accuracy is critical when calculations impact real-life decisions such as loan payments, health metrics, academic scores, or business performance. Even small errors can lead to incorrect conclusions or poor decision-making.
Reliable online calculators use verified formulas, standardized units, and consistent logic to ensure precise results. Quality tools are also regularly reviewed and updated to match modern standards.
I Love Calculator is built using industry-accepted formulas and best practices. Each calculator is designed for clarity, simplicity, and consistent accuracy across all devices.
Whether you are calculating BMI, EMI, GPA, percentages, or unit conversions, our tools are transparent, reliable, and easy to understand for students, professionals, and everyday users.