The complex numbers `z, iz ` and `z + iz`, where `z in C\ text(\{0})`, are plotted in the Argand plane, forming the vertices of a triangle.
The area of this triangle is given by
- `|z|`
- `|z| + |z|^2`
- `(|z|^2)/2`
- `|z|^2`
- `(sqrt 3 |z|^2)/2`
Show Worked Solution
| `text(Area)` | `= 1/2 b h` |
| `= 1/2 |z + iz – z| |z + iz – iz|` | |
| `= 1/2 |iz| |z|` | |
| `= 1/2 |i| |z|^2` | |
| `= (|z|^2)/2` |
`=> C`