(2+3i)+(-4+i) Simplify

Jasonbradley

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Jun 16, 2024

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Adding Complex Numbers: A Step-by-Step Guide

This article will guide you through the process of adding two complex numbers: (2 + 3i) + (-4 + i).

Understanding Complex Numbers

Complex numbers are numbers that extend the real number system by including the imaginary unit i, where i² = -1. A complex number is typically written in the form a + bi, where a and b are real numbers.

The Addition Process

Adding complex numbers is similar to adding binomials. We simply combine the real parts and the imaginary parts separately.

1. Identify the real and imaginary parts:

   • In (2 + 3i), the real part is 2 and the imaginary part is 3i.
   • In (-4 + i), the real part is -4 and the imaginary part is i.

2. Combine the real parts:

   • 2 + (-4) = -2

3. Combine the imaginary parts:

   • 3i + i = 4i

4. Write the simplified complex number:

   • The sum of the two complex numbers is -2 + 4i.

Conclusion

Therefore, (2 + 3i) + (-4 + i) = -2 + 4i. Remember, adding complex numbers involves combining the real parts and the imaginary parts separately. This approach allows us to simplify the expression and express the sum in the standard form a + bi.