Question

solve the equation by the square root property.
$(z + 2)^2 = -64$
the solution set is {}.
(simplify your answer. use a comma to separate answers as needed.)

Explanation:

Step1: Apply square root property

Take the square root of both sides: \( z + 2=\pm\sqrt{-64} \)

Step2: Simplify the square root

Since \( \sqrt{-64}=\sqrt{64}\times\sqrt{-1}=8i \) (where \( i \) is the imaginary unit, \( i^2 = - 1 \)), we have \( z + 2=\pm8i \)

Step3: Solve for z

Subtract 2 from both sides: \( z=-2\pm8i \)

Answer:

\(-2 + 8i, -2 - 8i\)