2x^3-11x^2+44x+27 if x=25/3-4i
Answers
Answer:
2
Step-by-step explanation:
2x^3-11x^2+44x+27 if x=25/3-4i
Given x = 25 / 3 – 4i
Rationalising the denominator we get
x = 25/3 – 4i x 3 + 4i / 3 + 4i
x = 25 (3 + 4i ) / 25
x = 3 + 4i
Now we need to find x^3 and x^2
So x^3 = (3 + 4i)^3
We know that
(a + b)^3 = a^3 + b^3 + 3ab(a + b)
= 27 + (-64 i) + 3.3.4i(3 + 4i)
= 27 – 64i + 36 I (3 + 4i)
= -117 + 44i
Now we need to find x^2 = (3 + 4i)^2
We know that
(a + b)^2 = a^2 + b^2 + 2ab
= (3)^2 + (4i)^2 + 2.3.4i
= 9 – 16 + 24i
= - 7 + 24i
Now we have the equation
f (x) = 2x^3 – 11x^2 + 44x + 27
= 2(- 117 + 44i) – 11(- 7 + 24i) + 44(3 + 24i) + 27
= - 234 + 88i + 77 – 264i + 132 + 176i + 2
= 234 + 236
f (x) = 2