To add two complex vectors, you add their corresponding real and imaginary components separately.
Here's a breakdown:
Let's say you have two complex vectors:
- Vector A: a + bi
- Vector B: c + di
Where:
- a and c are the real components.
- b and d are the imaginary components.
- 'i' represents the imaginary unit (√-1).
The resultant vector (Vector C) from adding Vector A and Vector B is calculated as follows:
Vector C = Vector A + Vector B = (a + c) + (b + d)i
In essence:
- The real component of the resultant vector (Vector C) is the sum of the real components of Vector A and Vector B (a + c).
- The imaginary component of the resultant vector (Vector C) is the sum of the imaginary components of Vector A and Vector B (b + d).
Example:
Let Vector A = 3 + 2i and Vector B = 1 - 4i. Then:
Vector C = (3 + 1) + (2 + (-4))i = 4 - 2i
In summary, you add the real parts together and the imaginary parts together separately to obtain the real and imaginary parts of the resultant vector.
