There are points in complex space. Among these points, there are
$z_{B} = \sqrt{3} - i$
$z_{C} = i$
$z_{E} = -\sqrt{3} - i$
The question says: Find $z_{H}$ where $\overrightarrow{HC}.\overrightarrow{EB} = 0$ and $||\overrightarrow{HC}|| = 3$
My solution:
So I did dot product between the two vectors $\overrightarrow{HC}$ and $\overrightarrow{EB}$
I found that $x_{H} = 0$
Then to find $y_{H}$:
||$\overrightarrow{HC}|| = 3$ means
$\sqrt{(y_{H} - 1)^{2}} = 3$
Here is the thing, that means it's absolute value
So
$\sqrt{(y_{H} - 1)^{2}} = \begin{cases} & \text{ } 3 \\ OR & \text{} - 3 \end{cases}$
That means $y_{H}$ is either $4$ or $-2$
So which value I take here?