%2B(3-2i)-in-standard-form.jpeg "(5+2i)+(3-2i) In Standard Form")
Adding Complex Numbers: (5 + 2i) + (3 - 2i)
This article will demonstrate how to add two complex numbers in standard form. We will work with the example: (5 + 2i) + (3 - 2i).
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 (i.e., i² = -1).
Adding Complex Numbers
To add complex numbers, we simply add the real parts and the imaginary parts separately.
1. Identify the real and imaginary parts:
- In (5 + 2i), 5 is the real part and 2 is the imaginary part.
- In (3 - 2i), 3 is the real part and -2 is the imaginary part.
2. Add the real parts:
- 5 + 3 = 8
3. Add the imaginary parts:
- 2 + (-2) = 0
4. Combine the results:
- The sum of the real parts is 8.
- The sum of the imaginary parts is 0.
Therefore, the sum of (5 + 2i) + (3 - 2i) in standard form is 8 + 0i, which simplifies to just 8.