%2B(7%2B3i)-in-standard-form.jpeg "(12-3i)+(7+3i) In Standard Form")
Adding Complex Numbers: (12-3i) + (7+3i)
This article will guide you through adding two complex numbers, (12-3i) and (7+3i), and expressing the result in standard form.
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
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.
- In (12 - 3i), the real part is 12 and the imaginary part is -3.
- In (7 + 3i), the real part is 7 and the imaginary part is 3.
Step 2: Add the real parts and the imaginary parts separately.
- Real part: 12 + 7 = 19
- Imaginary part: -3 + 3 = 0
Step 3: Combine the results to express the sum in standard form.
(12 - 3i) + (7 + 3i) = 19 + 0i
Since 0i is simply 0, the final answer in standard form is 19.
Conclusion
Adding complex numbers involves combining the real and imaginary components separately. By following the simple steps outlined above, you can easily find the sum of any two complex numbers and express the result in standard form (a + bi).