(-6+7i)+(6-7i)

Jasonbradley

2 min read

·

Jun 16, 2024

14

Share

Adding Complex Numbers: (-6 + 7i) + (6 - 7i)

This article will demonstrate how to add two complex numbers: (-6 + 7i) + (6 - 7i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where:

• a and b are real numbers
• i is the imaginary unit, defined as the square root of -1 (i² = -1)

Adding Complex Numbers

To add complex numbers, we simply add the real parts and the imaginary parts separately.

Step-by-Step Solution

1. Identify the real and imaginary parts:

   • (-6 + 7i): Real part = -6, Imaginary part = 7
   • (6 - 7i): Real part = 6, Imaginary part = -7

2. Add the real parts: -6 + 6 = 0

3. Add the imaginary parts: 7 - 7 = 0

4. Combine the results: 0 + 0i = 0

Conclusion

Therefore, the sum of the complex numbers (-6 + 7i) and (6 - 7i) is 0. This result highlights that adding a complex number and its conjugate (the number with the opposite sign for the imaginary part) always results in a real number.