%2B(5%2B3i).jpeg "(−4+10i)+(5+3i)")
Adding Complex Numbers: (−4+10i)+(5+3i)
This article will guide you through the process of adding two complex numbers: (−4+10i) 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.
Adding Complex Numbers
Adding complex numbers is straightforward. We simply add the real parts and the imaginary parts separately.
Step 1: Identify the real and imaginary parts of each complex number.
- For (−4+10i):
- Real part: -4
- Imaginary part: 10
- For (5+3i):
- Real part: 5
- Imaginary part: 3
Step 2: Add the real parts: -4 + 5 = 1
Step 3: Add the imaginary parts: 10 + 3 = 13
Step 4: Combine the results to get the final complex number: 1 + 13i
Conclusion
Therefore, the sum of (−4+10i) and (5+3i) is 1 + 13i. This process demonstrates the simplicity of adding complex numbers. It's important to remember that complex numbers are added by combining their real and imaginary components separately.