(-6-7i)+(2+6i)

Jasonbradley

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Jun 16, 2024

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Adding Complex Numbers: (-6 - 7i) + (2 + 6i)

This article explores the process of adding complex numbers, using the example of (-6 - 7i) + (2 + 6i).

Understanding Complex Numbers

Complex numbers are numbers that extend the real number system by introducing the imaginary unit i, where i² = -1. They are expressed in the form a + bi, where 'a' and 'b' are real numbers.

Adding Complex Numbers

To add complex numbers, we simply add the real and imaginary components separately. This is similar to how we add binomials in algebra.

Steps:

1. Identify the real and imaginary components:
   • (-6 - 7i): Real component = -6, Imaginary component = -7
   • (2 + 6i): Real component = 2, Imaginary component = 6
2. Add the real components: -6 + 2 = -4
3. Add the imaginary components: -7 + 6 = -1
4. Combine the results: -4 - i

Solution

Therefore, (-6 - 7i) + (2 + 6i) = -4 - i.

Visualizing Complex Numbers

Complex numbers can be visualized as points on a complex plane. The real component is represented on the horizontal axis (x-axis), and the imaginary component on the vertical axis (y-axis). Adding complex numbers can be viewed as vector addition on this plane.

Conclusion

Adding complex numbers is straightforward. We simply add the real and imaginary components separately. This understanding is essential for working with complex numbers in various mathematical and scientific fields.