Explanation

Complex numbers behave like points in the plane.

Distance between two complex numbers:
If z₁ = a + bi and z₂ = c + di,

Distance = √[(c − a)² + (d − b)²]

Midpoint:
Midpoint = ((a + c)/2) + ((b + d)/2)i

These formulas come from coordinate geometry.

Quiz

1. What formula is used to find distance?

2. What is the distance between 0 + 0i and 3 + 4i?

3. What is the midpoint of 2 + 2i and 4 + 6i?

4. Does distance use the Pythagorean Theorem?

5. Is the midpoint always halfway between two points?

Answer Key

1. Distance formula

2. 5

3. 3 + 4i

4. Yes

5. Yes