If z = -3 + V2, then prove that z4 + 5z^3+ 8z^2 + 72 +4 is equal to -29.
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Answer:
Given z=2−i
3
, ∴ z−2=−i
3
Squaring both sides, ∴ z
2
−4z+4=−3
∴ z
2
−4z=−7
Now z
4
−4z
2
+8z+35=(z
2
−4z+7)(z
2
+4z+5)
Thus z
4
−4z
2
+8z+35=0.
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