99 Percentile Qs Bank for JEE MainMathematicsComplex Number

. If , are the roots of the equation x^2-2 x+4=0 , then ^n+ ^n= ( n 3 ) for any n N

Options

A2^n
B2^ n+1
C2^ n-1
D2^ n-2

Correct answer

B. 2^ n+1

Step-by-step solution

Given quadratic equation x^2-2 x+4=0 having roots and . So, , = 2 4-16 2 = 2 2 3 i 2 =1 3 i gathered =2 ( 3 +i 3 ) and 2 ( (- 3 )+i (- 3 ) ) ^ n+ + ^ n t =2^ n t [ ( 3 +i 3 )^n . .+ ( (- 3 )+i (- 3 ) )^n ] =2^ n t [2 n 3 ]=2^ n+1 ( n 3 ) gathered

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