Assignment 5

1. Solve by completing the square.

a. x² + 4x + 5 = 0

b. x² - 3x + 6 = 0

c. x² + 2x + 3= 0

2. Solve using the quadratic formula.

a. x² + x + 5 = 0

b. x² + 4x + 8 = 0

c. x² - x + 5 = 0

3. Put in standard form (a + bi).

a. (2+3i) + (-1+ i)

b. (-1-4i)*(2-3i)

c. (3+i )-(1-2i)

d. (1+2i)/(1-3i)

e. (-2+5i)/(2+i)

4. Sketch and label in the complex plane

a. (1-2i), (2+3i), (4i), 3

b. The conjugates of the above

c. All z (that is, x+yi) with real part = 2.

d. All z with absolute value = 2.

5. If you drop a stone into the well in MacFarlane’s Castle, it takes 6 second until you hear the splash. How deep is the well?

6. What are the dimensions of the largest rectangular area you can fence with 150 feet of fencing, if you can use the side of your house for one side?

7. When are the roots of x² + ax + b complex? What does the sketch look like?