using quadratic formula to find roots of complex variable

Question

I need to find all complex number z such that $z^2+(-7-7i)z+49i=0$ while using the quadratic formula. I’ve got $z=\frac{(7+7i)\pm\sqrt{-147i}}{2}$ and then I don’t know what to do next. Can anyone help?

Answer 1

You should have $$z=\frac{(7+7i)\pm\sqrt{-\color{red}{98}i}}{2}=\frac{7+7i\pm7\sqrt{-2i}}{2}=\frac{7+7i\pm7(1-i)}{2}=7 \text{ or } 7i$$