Question

solve the equation -z² - 3z = 5 - 3z and re - express the answer as a complex number with the imaginary unit. (1 point)

Explanation:

Step1: Rearrange the equation

First, rewrite the equation $-z^{2}-3z = 5 - 3z$ to the standard - quadratic - form $az^{2}+bz + c = 0$. Add $3z$ to both sides, we get $-z^{2}-3z+3z=5 - 3z+3z$, which simplifies to $-z^{2}=5$, or $z^{2}=-5$.

Step2: Solve for z

Take the square - root of both sides. Recall that if $z^{2}=k$, then $z=\pm\sqrt{k}$. For $z^{2}=-5$, we have $z=\pm\sqrt{5}i$ since $\sqrt{-1}=i$.

Answer:

$z = \sqrt{5}i$ or $z=-\sqrt{5}i$