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  4. If x = 2 + 5i, then value of the expression x3 - 5x2 + 33x - 49 equals

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Q. If $x = 2 + 5i$, then value of the expression $x^3 - 5x^2 + 33x - 49$ equals

Complex Numbers and Quadratic Equations

Solution:

Given $x = 2 + 5i $
$ \Rightarrow x - 2 = 5i ...(i)$
$\Rightarrow x^2 - 4x + 29 = 0$ (squaring (i) both sides)
Now, $x^3 - 5x^2 + 33x - 49$
$= x (x^2 - 4x + 29) - 1 ( x^2 - 4x + 29) - 20$
$= x(0) - 1(0) - 20 = - 20$