Final answer:
The midpoint of a line segment between two points on the complex plane is found by averaging the real parts and the imaginary parts of the given complex numbers separately. Using the provided formula, one can calculate the exact position of the midpoint on the complex plane.
Step-by-step explanation:
To calculate the midpoint of the line segment that joins points p and q on the complex plane, you need to remember that each complex number is expressed in the form a + bi, where a is the real part and bi is the imaginary part. The midpoint of two complex numbers p = a + bi and q = c + di can be found by averaging their real and imaginary parts separately.
The formula for the midpoint M is given by:
M = \((\frac{a+c}{2}) + (\frac{b+d}{2})i\)
Let's go through this with an example. If we have p = 3 + 2i and q = 5 + 6i, the midpoint would be:
M = \((\frac{3+5}{2}) + (\frac{2+6}{2})i\) = (4) + (4)i = 4 + 4i