Question

What is the midpoint between z₁ = 3 + 9i and z₂ = 4 - 12i?

a. (0.5,-10.5)
b. (3.5,-1.5)
c. (-2,-2.5)
d. (6,-1.5)

Answer 1

The midpoint between the complex numbers z₁ = 3 + 9i and z₂ = 4 - 12i is found by averaging the real and imaginary parts separately, yielding the midpoint (3.5, -1.5).Option B is the correct answer.

Step-by-step explanation:

To find the midpoint between two complex numbers z₁ = 3 + 9i and z₂ = 4 - 12i, we use the midpoint formula for complex numbers, which is similar to finding the midpoint between two points in the coordinate plane. The midpoint M is given by the formula M = ½(z₁ + z₂). Therefore, the real part of the midpoint is (½ × (3 + 4)) and the imaginary part is (½ × (9 - 12)i).

The calculations are as follows:

1. Real part: ½ × (3 + 4) = ½ × 7 = 3.5
2. Imaginary part: ½ × (9 - 12) = ½ × (-3) = -1.5i
   

Therefore, the midpoint M is (3.5, -1.5), corresponding to option b.