What is the S to the 10-th power, if S is the sum of the solutions of the equation 2x2 - 2ix +10=0, where i=√(-1)
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2x² -2ix + 10 = 0 is a type of complex quadratic equation .
sum of roots ( solutions) = - coefficient of x / coefficient of x²
but ,
A/c to Q ,
S = sum of solutions
so,
S = - ( coefficient of x)/( coefficient of x²)
S = - ( -2i )/(2) = i
S = i
Q ask ,
S^10 = ?
S^10 = (i)^10 = { √(-1)}^10
= { ( -1)½ }^10
= ( -1 )^5
= ( -1)^4 × (-1)
= 1 × ( -1)
= -1
sum of roots ( solutions) = - coefficient of x / coefficient of x²
but ,
A/c to Q ,
S = sum of solutions
so,
S = - ( coefficient of x)/( coefficient of x²)
S = - ( -2i )/(2) = i
S = i
Q ask ,
S^10 = ?
S^10 = (i)^10 = { √(-1)}^10
= { ( -1)½ }^10
= ( -1 )^5
= ( -1)^4 × (-1)
= 1 × ( -1)
= -1
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