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Find the value of x4 + 9x3 + 35x2 - x + 4, if x = -5 +  √-4

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x = -5 + √-4

x + 5 = √-4

x + 5 = √4 √-1

x + 5 = 2i

(x + 5)2 = 4i2

x2 + 10x + 25 = 4(-1) ….[∵ i2 = -1]

x2 + 10x + 29 = 0 …..(i)

Dividend = Divisor × Quotient + Remainder

x4 + 9x3 + 35x2 – x + 4 = (x2 + 10x + 29) (x2 – x + 16) – 132x – 460

= 0.(x2 – x + 16) – 132x – 460 …..[From (i)]

= -132 (-5 + 2i) – 460

= 660 – 264i – 460

= 200 – 264i

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