To find the sum or difference of the complex numbers in standard form, we’ll work with the given numbers: 3 + 3i and 6 + i.
Finding the Sum
The sum of two complex numbers is calculated by adding their real parts and their imaginary parts separately.
For our example:
- Real parts: 3 (from 3 + 3i) + 6 (from 6 + i) = 3 + 6 = 9
- Imaginary parts: 3i (from 3 + 3i) + 1i (from 6 + i) = 3i + 1i = 4i
Combining both results, the sum of the complex numbers is:
Sum: 9 + 4i
Finding the Difference
To find the difference, we subtract the real parts and the imaginary parts:
For our example:
- Real parts: 3 (from 3 + 3i) – 6 (from 6 + i) = 3 – 6 = -3
- Imaginary parts: 3i (from 3 + 3i) – 1i (from 6 + i) = 3i – 1i = 2i
Combining both results, the difference of the complex numbers is:
Difference: -3 + 2i
To conclude, when you add the complex numbers 3 + 3i and 6 + i, you get 9 + 4i. When you subtract 6 + i from 3 + 3i, the result is -3 + 2i.