Maths · Argand diagram
Interpret the following equations geometrically on the Argand plane.
Interpret the following equations geometrically on the Argand plane. \( \mathbf{1}<|\boldsymbol{z}-\mathbf{2}-\mathbf{3} \boldsymbol{i}|<\mathbf{4} \)
- A. Annular
- B. Straight line
- C. A point
- D. Ringg
Step-by-step solution
The inequality 1 < |z - (2+3i)| < 4 represents all points z whose distance from the point (2,3) in the complex plane is between 1 and 4. This defines the region between two circles centered at (2,3) with radii 1 and 4, excluding the boundaries. This region is an annulus (ring-shaped area).