Solve the equation $z^{\wedge} 2+4 z+13=0$, where $z$ is a complex number.

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∻Solution by Steps∻ ‖ step 1 ⋮ To solve the quadratic equation $z^2 + 4z + 13 = 0$ for $z$, we use the quadratic formula $z = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 1$, $b = 4$, and $c = 13$. ‖ ‖ step 2 ⋮ Calculate the discriminant: $b^2 - 4ac = 4^2 - 4 \cdot 1 \cdot 13 = 16 - 52 = -36$. ‖ ‖ step 3 ⋮ Since the discriminant is negative, the solutions will be complex numbers. ‖ ‖ step 4 ⋮ Substitute the values into the quadratic formula: $z = \frac{-4 \pm \sqrt{-36}}{2 \cdot 1} = \frac{-4 \pm 6i}{2}$. ‖ ‖ step 5 ⋮ Simplify the expression: $z = \frac{-4}{2} \pm \frac{6i}{2} = -2 \pm 3i$. ‖ ∻Answer∻ ⚹ The solutions to the equation $z^2 + 4z + 13 = 0$ are $z = -2 + 3i$ and $z = -2 - 3i$. ⚹ ∻Key Concept∻ ⚹Solving quadratic equations with complex solutions⚹ ∻Explanation∻ ⚹When the discriminant of a quadratic equation is negative, the solutions are complex numbers. The quadratic formula can be used to find these solutions.⚹◊What is the solution to the equation $z^{2}+4z+13=0$ where $z$ is a complex number?⍭ Generate me a similar question◊

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