If $$x=2+5i$$ then the value of $$x3$$−$$5x2+33x$$−$$19$$ is equal to

Question

If $$x=2+5i$$ then the value of $$x3$$−$$5x2+33x$$−$$19$$  is equal to

Infinity Learn · Accepted Answer

$$x=2+5i$$ ⇒ x−$$2=5i$$⇒ $$(x$$−$$2)2=(5i)2$$⇒$$x2$$−$$4x+4=$$−$$25$$⇒$$x2$$−$$4x+29=0$$ We now divide $$x3$$−$$5x2+33x$$−$$19$$ by $$x2$$−$$4x+29$$                              $$x-1$$ $$x2$$−$$4x+29x3$$−$$5x2+33x$$−$$19$$                          $$x3$$−$$4x2+29x$$  $$-$$ ⊕ $$-$$ $$___________$$ −$$x2+4x$$−$$19$$−$$x2+4x$$−$$29-$$ ⊕ $$-$$  $$_____________$$                       $$10$$  Thus $$x3$$−$$5x2+33x$$−$$19=(x$$−$$1)x2$$−$$4x+29+10=(x$$−$$1)(0)+10=10$$

If $x = 2 + 5 i$ then the value of $x^{3} - 5 x^{2} +$ $33 x - 19$ is equal to

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If x=2+5i then the value of x3−5x2+33x−19 is equal to

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If $x = 2 + 5 i$ then the value of $x^{3} - 5 x^{2} +$ $33 x - 19$ is equal to