Solve z ^ { 2 } + i z + 6 = 0

Evaluate

z^{2} + i z + 6 = 0

Substitute a= 1,b= i and c= 6 into the quadratic formula z = \frac{- b \pm b ^{2} - 4 a c}{2 a}

z = \frac{- i \pm i ^{2} - 4 \times 6}{2}

Simplify the expression

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z = \frac{- i \pm - 25}{2}

Simplify the radical expression

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z = \frac{- i \pm 5 i}{2}

Separate the equation into 2 possible cases

z = \frac{- i + 5 i}{2} z = \frac{- i - 5 i}{2}

Simplify the expression

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z = 2 i z = \frac{- i - 5 i}{2}

Simplify the expression

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z = 2 i z = - 3 i

Solution

z_{1} = - 3 i, z_{2} = 2 i

Solve the equation