# Q.If `x=1+i;` then the value of the expression `x^4-4x^3+7x^2-6x+3` is:- A) -1 B) 1 C) 2 D) None of these

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Expert Answers

justaguide | Certified Educator

It is given that x = 1 + i

x^4 - 4x^3 + 7x^2 - 6x + 3

=> x^4 - 3x^3 + 3x^2 - x^3 + 3x^2 - 3x + x^2 - 3x + 3

=> x^2(x^2 - 3x + 3) - x(x^2 -3x + 3) +1(x^2 - 3x + 3)

=> (x^2 - x + 1)(x^2 - 3x + 3)

Substitute x = 1 + i

=> ((1 + i)^2 - (1 + i) + 1)((1 + i)^2 - 3(1 + i) + 3)

=> (1 - 1 + 2i - 1 - i + 1)(1 - 1 + 2i - 3 - 3i + 3)

=> i*-i

=> 1

**The correct answer is option B**