Q16 of 153 Page 13

Evaluate the following :

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

Given:


⇒ x=-1+i


⇒ x+1=i


⇒ (x+1)4=(i)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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