(-4+2i)+(6-3i)

Jasonbradley

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Jun 16, 2024

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Adding Complex Numbers: (-4 + 2i) + (6 - 3i)

This article will demonstrate how to add two complex numbers: (-4 + 2i) + (6 - 3i).

Understanding Complex Numbers

Complex numbers are numbers that consist of two parts: a real part and an imaginary part. They are typically written in the form a + bi, where:

• a is the real part (a real number)
• b is the imaginary part (a real number)
• 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 add the imaginary parts separately.

Step 1: Separate the real and imaginary parts

• (-4 + 2i) has a real part of -4 and an imaginary part of 2.
• (6 - 3i) has a real part of 6 and an imaginary part of -3.

Step 2: Add the real parts and the imaginary parts

• Real part: -4 + 6 = 2
• Imaginary part: 2 + (-3) = -1

Step 3: Combine the results

The sum of (-4 + 2i) + (6 - 3i) is 2 - i.

Conclusion

Adding complex numbers is straightforward. We simply combine the real and imaginary components separately. In the case of (-4 + 2i) + (6 - 3i), the sum is 2 - i.