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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 $
$\Rightarrow \, x-2=5i$
$\Rightarrow \, x^{2}-4x+29=0$
Now, $x^{3} - 5x^{2} + 33x - 49$
$=x\left(x^{2}-4x+29\right)-1\left(x^{2}-4x+29\right)-20$
$=-20$