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Evaluate the following : x4 + 4x3 + 6x2 + 4x + 9, when x = - 1 + i√2

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Best answer

Given: 

⇒ x=-1+i i√2

⇒ x+1=i i√2

⇒ (x+1)4=(i \(\sqrt{2})^4 \)

⇒ x4+4x3+6x2+4x+1=2i4 

We know that i2=-1

⇒ x4+4x3+6x2+4x+1=2(-1)2 

⇒ x4+4x3+6x2+4x+1=2 

⇒ x4+4x3+6x2+4x+1+8=2+8 

⇒ x4+4x3+6x2+4x+9=10 

∴ x4+4x3+6x2+4x+9=10

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