1. **Problem statement:** What geometric effect does multiplication by $-i$ have on a complex number? 2. **Recall the properties of multiplication by $i$:** Multiplying a complex number by $i$ corresponds to a rotation by 90 degrees counterclockwise in the complex plane. 3. **Effect of multiplication by $-i$:** Since $-i = -1 \times i$, multiplying by $-i$ is equivalent to multiplying by $i$ and then by $-1$. 4. **Step-by-step geometric interpretation:** - Multiplying by $i$ rotates the complex number 90 degrees counterclockwise. - Multiplying by $-1$ reflects the complex number through the origin (rotates by 180 degrees). 5. **Combining these effects:** - Rotation by 90 degrees counterclockwise followed by rotation by 180 degrees is equivalent to rotation by $90 + 180 = 270$ degrees counterclockwise. - Rotation by 270 degrees counterclockwise is the same as rotation by 90 degrees clockwise. 6. **Final conclusion:** Multiplying a complex number by $-i$ rotates it by 90 degrees clockwise in the complex plane. This means the geometric effect of multiplication by $-i$ is a 90-degree clockwise rotation about the origin.