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Exercises for Chapter II Sections 6 and 7
For problems 1 - 8 give the magnitudes, real parts, and imaginary parts to two decimal places and the arguments in radians to four decimal places.
1. Let 
Give the polar form (i.e., 
form) for each of the
following products. Compare your answers to the exact values obtained in
Problem 1 of Exercises for Chapter 2 Sections 1 and 2.
(a) CD; (b) CE; (c) CF; (d) C2.
2. Let 
(a) Use the yx key to find a B = A1/5 in polar form.
(b) Find in polar form CB, C2B, C3B, C4B, and C5B.
(c) Compare your answers with the exact values obtained in Problem 19 of Exercises for Chapter 2 Sections 1 and 2.
3. Find the polar form for 5 fifth roots of 249.47e0.7493i.
4. Find the polar form for 7 seventh roots of 8274.85e-0.4444i.
5. Convert the following polar forms to rectangular form a + bi.
(f) Compare your answers with the exact values obtained in Problem 1 of Exercises for Chapter 2 Sections 3, 4, and 5.
6. Convert the following rectangular forms to polar form 
(a) 1 + i;
(b) 7i;
(c) 
(d) -3;
(e) -4 - 4i.
(f) Compare your answers with the exact values obtained in Problem 2 of Exercises for Chapter 2 Sections 3, 4, and 5.
7. Find complex numbers in polar and rectangular form with magnitude 1 and arguements equal to those listed below but converted to radians.
(a) 105o; (b) 15o; (c) 225o; (d) 135o; (e) 195o.
(f) Compare your answers with the exact values obtained in Problem 16 of Exercises for Chapter 2 Sections 3, 4, and 5.
8. Find the rectangular form of 
by entering 
then pressing the square root key. Compare your answers with the
exact values optained in
Problem 32 of Exercises for Chapter 2 Sections 3, 4, and 5.
For problems 9 - 12 let A = 3.47 - 6.52i, B = 4.32e1.1275i, C = -8.46 + 3.92i and D = 0.39e-2.0727i. Evaluate the given expressions and leave your answers in both polar and rectangular form. Give the magnitudes, real parts, and imaginary parts to two decimal places and the arguments in radians to four decimal places. HINT: It may be helpful to store the values of A, B, C, and D in your calculator memory.
9. (a) (A + B - C)D;
(b) 
(c) (A2 - C2)D;
(d) (A + C)3D.
10. (a) (A + B)(C - D);
(b) 
(c) (A3 + C3)D
(d) (A - C)2D.
11. Find the distance between A and B.
12. Find the distance between C and D.
In navigation directions are called bearings and are measured in degrees clockwise from north. Thus, if you are traveling east, you are traveling on a bearing of 90o; and if you are traveling south west, you are traveling on a bearing of 225o. For problems 13 and 14 give directions as bearings to the nearest degree and distances as miles to the nearest tenth of a mile.
13. A Coast Guard patrol boat leave the Coast Guard station and travels 13.1 miles on a bearing of 37o. It then turns to a bearing of 106o and travels 19.1 miles. From there it travels 13.2 miles on a bearing of 250o at which time it receives a distress call from a fishing boat. To reach the fishing boat it travels 11.4 miles on a bearing of 348o.
(a) Covert all of the bearings above to angles measured counterclockwise from east.
(b) There is an injured crewman on the fishing boat and the
Coast Guard medic decides he should be helicoptered to a
hospital. What distance and bearing should the helicopter
fly from the Coast Guard station to the fishing boat?
HINT: See Calculator Example 2.6.3.
(c) It is known that the nearest hospital is 19.5 miles on
a bearing of 166o from the Coast Guard station. What distance
and bearing must the helicopter fly from the fishing boat to the hospital?
14. A geological team leaves their base camp in a jeep and travel across the desert for 3.1 miles on a bearing of 27o. From there they travel for 6.7 miles on a bearing of 257o. They leave that location on a bearing of 146o, but their jeep breaks down after 3.2 miles. They radio the the base camp for a second jeep to come pick them up.
(a) What direction and distance must the second jeep travel from the base camp to reach the stranded team?
(b) It is known that the nearest repair facility is 6.4
miles on a bearing of 229o from the base camp. If the decision is
made to tow the disabled jeep directly to the repair facility,
what direction and distance should they travel from the site
of the breakdown?
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