| 3. (a) Here are the first few iterates. |
| c = -2: -2, 2, 2, and so on. All other iterates are 2. |
| c = -1: -1, 0, -1, 0, and so on. All iterates cycle between -1 and 0. |
| c = 1: 1, 2, 5. By the escape criterion, the iterates escape to infinity. |
| c = i: i, -1+i, -i, -1+i, -i, -1+i, and so on. All iterates cycle between -1+i and -i |
| Only c = 1 does not belong to the Mandelbrot set. |
| (b) Here are the first few iterates. |
| c = -2: -2, -10, -1002 |
| c = -1: -1, -2, -9, -730 |
| c = 1: -1, -2, -9, -730 |
| c = i: i, 0, i, 0, and so on. All iterates cycle between i and 0. |
| Only c = i belongs to the z3 + c Mandelbrot set. |
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