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

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