The image shows a graph of a parabola with a focus of \((3,4)\) and a directrix \(y=2\), and of a line given by \(y=4\). Find and verify the points where the parabola and the line intersect.

Write an equation whose graph is a line perpendicular to the graph of \(y=4\) and that passes through the point \((2,5)\).

Find the solution(s) to each equation.

1. \(x^2-6x+8=0\)
2. \(x^2-6x+9=0\)
3. \(x^2-6x+10=0\)

Write each expression in the form \(a+bi\), where \(a\) and \(b\) are real numbers.

1. \(5i^2\)

2. \(i^2 \boldcdot i^2\)

3. \((\text-3i)^2\)

4. \(7 \boldcdot 4i\)

5. \((5+4i) - (\text-3 + 2i)\)