Risolvere in C le seguenti equazioni. √ z=0 1. z|z|2 − (1 + 4 3)i¯ h p √ √ 0, ± 1 + 4 3 22 + h 2. z 3 z¯ + 3i|z|2 = 0 4. |z|2 = −iz 2 i √ 0, ± √32 (−1 + i) [x + ix, x ∈ R] 5. z|z| = 5z − 6 [2, 3, −6] 6. |z|2 + z = 4 − 2i [−2i, −1 − 2i] h i √ 0, ± 23 − 32 i 1−i 1+i 8. z 2 − 2z + 2 = 0 [1 ± i] h i √ −3± 13 i 2 9. z 2 + 3iz + 1 = 0 √ [i, (−1 − 2)i] h √ √ i 2 ± 2 + 22 i 10. z|z| − 2z + i = 0 11. z 2 |z|2 = i h √ i 7 1 ± 2 − 2i 2 12. z + i¯ z=1 13. z 2 − (4 + i)z + 4 + 2i = 0 14. z 6 + 2z 3 − 3 = 0 15. z 3 = 3 − 3i 16. (z 2 − 4)(¯ z 2 + i) = 0 17. iz 2 − |z|2 = 0 18. z 3 − i(z − 2)3 = 0 19. z 4 − z z¯ − 2 = 0 20. z 4 + (1 − i)z 2 − i = 0 21. (z + 2)4 = (z − 1)4 i 2 i 2 [−1, 21 + iy, y ∈ R] 3. |z 2 − 1| = |z + z 2 | 7. (z + i)3 = √ h 1, − 21 ± √ √ 3 3 i, 3 12 ± 2 [2, 2 + i] i √ √ 3 3 i ,− 3 2 h√ i √ √ 7 15 23 6 18ei 12 π , 6 18ei 12 π , 6 18ei 12 π h √ 2 (1 2 ± 2, ± i + i) [x − xi, x ∈ R] √ [1 + i, 1 − (2 ± 3)i] √ √ [± 2, ± 2i] √ [±i, ± 2 (1 2 + i)] [− 12 , −1±3i ] 2
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