Final answer:
The midpoint of the segment connecting complex numbers z1 = 3 − 17i and z2 = −9 − 3i is −3 − 10i, found by averaging the real and imaginary parts of the two complex numbers.
Step-by-step explanation:
To find the midpoint of the segment that connects two complex numbers z1 and z2, we can treat the complex numbers as points in a two-dimensional plane. Each complex number has a real part and an imaginary part, which correspond to the x and y coordinates, respectively, in the complex plane.
The midpoint M of the segment connecting z1 and z2 can be found using the midpoint formula for coordinates:
- M_real = (z1_real + z2_real) / 2
- M_imaginary = (z1_imaginary + z2_imaginary) / 2
For z1 = 3 − 17i and z2 = −9 − 3i, the midpoint M is calculated as follows:
- M_real = (3 + (−9)) / 2 = (−6) / 2 = −3
- M_imaginary = (−17 + (−3)) / 2 = (−20) / 2 = −10i
Therefore, the midpoint M of the segment connecting z1 and z2 on the complex plane is −3 − 10i.