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(5-2i)+(-13-8i)

2 min read Jun 16, 2024
(5-2i)+(-13-8i)

Adding Complex Numbers: (5 - 2i) + (-13 - 8i)

This article will walk you through the process of adding two complex numbers: (5 - 2i) and (-13 - 8i).

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 of each complex number:

    • (5 - 2i): Real part = 5, Imaginary part = -2
    • (-13 - 8i): Real part = -13, Imaginary part = -8

  2. Add the real parts:

    • 5 + (-13) = -8

  3. Add the imaginary parts:

    • -2 + (-8) = -10

  4. Combine the results to form the final complex number:

    • -8 - 10i

Conclusion

Therefore, the sum of (5 - 2i) and (-13 - 8i) is -8 - 10i.

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