What are the solutions to the equation z^2-3z+9=0 ?

The solutions to the equation z^2-3z+9=0 are z= 3/2+i(3sqrt(3))/2 ,z= 3/2-i(3sqrt(3))/2

Find the zeros of z^2-3z+9=0

The zeros of z^2-3z+9=0 are z= 3/2+i(3sqrt(3))/2 ,z= 3/2-i(3sqrt(3))/2

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z^{2} - 3 z + 9 = 0

z = \frac{3}{2} + i \frac{3 3}{2}, z = \frac{3}{2} - i \frac{3 3}{2}

Solution steps

z^{2} - 3 z + 9 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot 9}{2 \cdot 1}

Simplify

(- 3)^{2} - 4 \cdot 1 \cdot 9 : 33 i

z_{1, 2} = \frac{- ( - 3 ) \pm 3 3 i}{2 \cdot 1}

Separate the solutions

z_{1} = \frac{- ( - 3 ) + 3 3 i}{2 \cdot 1}, z_{2} = \frac{- ( - 3 ) - 3 3 i}{2 \cdot 1}

z = \frac{- ( - 3 ) + 3 3 i}{2 \cdot 1} : \frac{3}{2} + i \frac{3 3}{2}

z = \frac{- ( - 3 ) - 3 3 i}{2 \cdot 1} : \frac{3}{2} - i \frac{3 3}{2}

The solutions to the quadratic equation are:

z = \frac{3}{2} + i \frac{3 3}{2}, z = \frac{3}{2} - i \frac{3 3}{2}

(x - 4)^{2} + 5 = 0

- x^{2} + 7 x + 4 = 0

49 x^{2} + 9 = 0

8 x^{2} + 16 x + 6 = 0

4 x^{2} + 8 x + 2

What are the solutions to the equation z^2-3z+9=0 ?
The solutions to the equation z^2-3z+9=0 are z= 3/2+i(3sqrt(3))/2 ,z= 3/2-i(3sqrt(3))/2
Find the zeros of z^2-3z+9=0
The zeros of z^2-3z+9=0 are z= 3/2+i(3sqrt(3))/2 ,z= 3/2-i(3sqrt(3))/2