Question

solve the equation -z^2 - 3z = 5 - 3z and re - express the answer as a complex number with the imaginary unit. (1 point)

Explanation:

Step1: Rearrange the equation

Rearrange the equation \(-z^{2}-3z = 5 - 3z\) to the standard - quadratic form \(az^{2}+bz + c = 0\).
Adding \(z^{2}\) and \(3z\) to both sides, we get \(z^{2}+5=0\).

Step2: Solve for \(z\)

Subtract 5 from both sides: \(z^{2}=-5\).
Taking the square - root of both sides, \(z=\pm\sqrt{-5}\).
Since \(\sqrt{-1}=i\), we can rewrite \(\sqrt{-5}\) as \(\sqrt{5}i\). So \(z = \pm\sqrt{5}i\).

Answer:

\(z=\sqrt{5}i\) or \(z =-\sqrt{5}i\)