Math, asked by nusrath8611, 1 year ago

2x^3-11x^2+44x+27 if x=25/3-4i

Answers

Answered by knjroopa
17

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

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