(8+3i)+(-6-12i)

2 min read Jun 16, 2024
(8+3i)+(-6-12i)

Adding Complex Numbers: (8 + 3i) + (-6 - 12i)

This article will demonstrate how to add two complex numbers: (8 + 3i) + (-6 - 12i).

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.

  • Real Part: The real part of a complex number is the constant term (a).
  • Imaginary Part: The imaginary part of a complex number is the coefficient of i (b).

Adding Complex Numbers

To add complex numbers, we simply add the real parts and the imaginary parts separately.

Step 1: Identify the real and imaginary parts of each complex number:

  • (8 + 3i): Real part = 8, Imaginary part = 3
  • (-6 - 12i): Real part = -6, Imaginary part = -12

Step 2: Add the real parts: 8 + (-6) = 2

Step 3: Add the imaginary parts: 3 + (-12) = -9

Step 4: Combine the results: 2 + (-9)i = 2 - 9i

Therefore, (8 + 3i) + (-6 - 12i) = 2 - 9i.

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