Complex Conjugate Calculator

This Complex Conjugate Calculator allows users to input real and imaginary parts of a complex number to compute its conjugate and magnitude with precise formatting.

Use Our Complex Conjugate Calculator

Guide to Using the Complex Conjugate Calculator

This step-by-step guide will help you understand how to use the Complex Conjugate Calculator to compute the complex conjugate of a given complex number, along with its magnitude. Follow the instructions below to make the most of this tool.

Step 1: Input the Real Part

  1. Locate the input field labeled Real Part (a).
  2. Enter the real part of your complex number in the provided field. Make sure it is a valid number as the validation requires a numeric input. This field is mandatory, so ensure it is filled before proceeding.

Step 2: Input the Imaginary Part

  1. Find the input field labeled Imaginary Part (b).
  2. Enter the imaginary part of your complex number. Again, ensure that your input is a number. This input is also required to continue the calculation.

Step 3: Understand the Result Fields

Once you have entered both parts of the complex number, the calculator will automatically display several results, each showing a different aspect of the complex conjugate calculation.

Result Field: Conjugate Real Part

  1. Identify the result labeled Conjugate Real Part.
  2. This value is the same as the real part you entered, and it represents the real component of the complex conjugate. It is formatted to two decimal places.

Result Field: Conjugate Imaginary Part

  1. Check the result labeled Conjugate Imaginary Part.
  2. This is the negated value of the imaginary part you provided. The signed version is displayed with two decimal places, representing the imaginary component of the complex conjugate.

Result Field: Complete Complex Conjugate

  1. Observe the Complete Complex Conjugate result.
  2. The result is presented in the format z̄ = a – bi or z̄ = a + bi, where a and b are the real and imaginary parts, respectively. The operator between them is determined based on the sign of the imaginary part.

Result Field: Magnitude

  1. Finally, view the Magnitude result.
  2. This value is the magnitude of the original complex number, calculated as the square root of the sum of the squares of the real and imaginary parts. It is presented with four decimal places for precision.

By following these steps, you can efficiently use the Complex Conjugate Calculator to obtain the required computations. Ensure that all inputs are correct to achieve accurate results.