x = -5 + √-4

x + 5 = √-4

x + 5 = √4 √-1

x + 5 = 2i

(x + 5)^{2} = 4i^{2}

x^{2} + 10x + 25 = 4(-1) …**.[∵ i**^{2} = -1]

x^{2} + 10x + 29 = 0 **…..(i)**

Dividend = Divisor × Quotient + Remainder

x^{4} + 9x^{3} + 35x^{2} – x + 4 = (x^{2} + 10x + 29) (x^{2} – x + 16) – 132x – 460

= 0.(x^{2} – x + 16) – 132x – 460 **…..[From (i)]**

= -132 (-5 + 2i) – 460

= 660 – 264i – 460

= 200 – 264i