Question

If z = -3 + V2, then prove that z4 + 5z^3+ 8z^2 + 72 +4 is equal to -29.

Answer 1

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.