(3-2i)+(5+3i)

Jasonbradley

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Jun 16, 2024

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Adding Complex Numbers: (3-2i)+(5+3i)

This article will walk you through the process of adding two complex numbers: (3-2i) and (5+3i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, defined as the square root of -1 (i² = -1).

Adding Complex Numbers

Adding complex numbers is a simple process that involves adding the real and imaginary components separately.

1. Identify the real and imaginary components:

   • In (3-2i), the real component is 3 and the imaginary component is -2i.
   • In (5+3i), the real component is 5 and the imaginary component is 3i.

2. Add the real components:

   • 3 + 5 = 8

3. Add the imaginary components:

   • -2i + 3i = i

4. Combine the results:

   • The sum of (3-2i) and (5+3i) is 8 + i.

Conclusion

Therefore, the sum of the complex numbers (3-2i) and (5+3i) is 8 + i. This demonstrates the straightforward nature of adding complex numbers by treating the real and imaginary components independently.