Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is $\displaystyle 2$.

Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is $\displaystyle -5$.

$\displaystyle (2, -5)$ are the coordinates for point L.

Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is $\displaystyle 7$.

Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is $\displaystyle 4$.

$\displaystyle (7, 4)$ are the coordinates for point M.

Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is above the point. The x-coordinate is $\displaystyle -6$.

Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is $\displaystyle -3$.

$\displaystyle (-6, -3)$ are the coordinates for point K.

First, we need to find the slope of the above line. 

The slope of a line. given two points $\displaystyle (x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula

$\displaystyle m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $\displaystyle x_{1}=-4, y_{1}=x_{2}= 0, y_{2}=8$:

$\displaystyle m = \frac{8-0}{0-(-4)} = \frac{8}{4} = 2$

The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be $\displaystyle m = -\frac{1}{2}$. Since we want this line to have the same $\displaystyle y$-intercept as the first line, which is the point $\displaystyle (0,8)$, we can substitute $\displaystyle m = -\frac{1}{2}$ and $\displaystyle b = 8$ in the slope-intercept form:

$\displaystyle y = mx + b$

$\displaystyle y = - \frac{1}{2}x + 8$

One way to answer this is to first find the equation of the line. 

The slope of a line. given two points $\displaystyle (x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula

$\displaystyle m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $\displaystyle x_{1}=-6, y_{1}=x_{2}= 0, y_{2}=18$:

$\displaystyle m = \frac{18-0}{0-(-6)} = \frac{18}{6} = 3$

The line has slope 3 and $\displaystyle y$-intercept $\displaystyle (0,18)$, so we can substitute $\displaystyle m = 3, b = 18$ in the slope-intercept form:

$\displaystyle y = mx+b$

$\displaystyle y = 3x+18$

Now substitute 4 for $\displaystyle y$ and $\displaystyle N$ for $\displaystyle x$ and solve for $\displaystyle N$:

$\displaystyle 4= 3N+18$

$\displaystyle -14 =3N$

$\displaystyle N = -\frac{14}{3}= -4\frac{2}{3}$

FOIL the product out:

$\displaystyle \left (7 - 2i \right )\left (7 - 3i \right )$

$\displaystyle = 7 \cdot 7 - 7 \cdot 3i - 7 \cdot 2i + 2i \cdot 3i$

$\displaystyle = 49 -21i - 14i + 6 i^{2}$

$\displaystyle = 49 -21i - 14i + 6 (-1)$

$\displaystyle = 49 -6 -21i - 14i$

$\displaystyle = 43 -35i$

Use the square of a binomial pattern to multiply this:

$\displaystyle \left ( 8 - 3i\right ) ^{2}$

$\displaystyle = 8 ^{2}- 2 \cdot8\cdot3i + \left ( 3i\right )^{2}$

$\displaystyle = 64- 48i + 3^{2}i^{2}$

$\displaystyle = 64- 48i + 9 (-1)$

$\displaystyle = 64-9 - 48i$

$\displaystyle = 55 - 48i$

This is a product of an imaginary number and its complex conjugate, so it can be evaluated using this formula:

$\displaystyle \left (a + bi \right )\left (a -bi \right ) = a^{2} + b ^{2}$

$\displaystyle \left (1.1 + 0.6i \right )\left (1.1 -0.6 i \right ) = 1.1^{2} + 0.6 ^{2} = 1.21 + 0.36 = 1.57$

This is a product of an imaginary number and its complex conjugate, so it can be evaluated using this formula:

$\displaystyle \left (a - bi \right )\left (a +bi \right ) = a^{2} + b ^{2}$

$\displaystyle \left (5 - 3i \right )\left (5 +3i \right ) = 5 ^{2} + 3 ^{2}= 25 + 9 = 34$

$\displaystyle a*b = a ^{5}-b^{3}$

$\displaystyle \left (2 i \right )* \left (3i \right ) = \left (2 i \right ) ^{5}-\left (3i \right ) ^{3}$

$\displaystyle = 2^{5} i^{5} - 3^{3} i ^{3}$

$\displaystyle = 32\cdot i^{4} \cdot i - 27 \cdot (-i )$

$\displaystyle = 32\cdot 1 \cdot i +27 i$

$\displaystyle = 32 i +27 i$

$\displaystyle = 59 i$