How is solve in complex equation z+1/z=1?

Asked on by econominty

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to subtract 1 both sides to preserve the equation, such that:

z + 1/z - 1 = 0

You need to bring all terms to a common denominator:

`z^2 + 1 - z = 0 =gt z^2 - z + 1 = 0`

You need to use quadratic formula to find the roots such that:

`z_(1,2) = (1+-sqrt(1-4))/2 =gt z_(1,2) = (1+-sqrt(-3))/2`

Using the theory of complex numbers yields:

`z_(1) =(1+isqrt3)/2 ; z_(2) =(1-isqrt3)/2`

Hence, the complex solutions to the equation are `z_(1) =(1+isqrt3)/2 ; z_(2) =(1-isqrt3)/2.`

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