7.5 Homework Problems: Mathematical Functions and Converting Between Polar and Rectangular
1. Perform the requested operation and simplify as much as possible. Leave answers in polar form
a. (5.12 + 7.2i) · (3.15 – 5.38i)
b. (2 – 4i) · (3 + 8i)
c. [(5 + i) · (4 – 3i)] · (1 + 5i)
d. (2.86 ∠ 38.2°)(1.55 ∠ 21.1°)
e. (34∠−45°) · (59∠−45°)
f. (28.4 ∠ 56°)(75.3 ∠ -35°)
g. (24 ∠ 50°) ÷ (12 ∠ 30°)
h. (20.2 ∠ −48°)(2.6 ∠ 155°)
i. (16.5 ∠ −235°)(24.6 ∠ −135°)
j. (24 ∠ 50° + 10 ∠ 37°)(12 ∠ -45° + 6 ∠ 67°)
2. Find the magnitude and direction with respect to the positive x-axis, of the vectors shown below. (Hint: Convert to rectangular, add and convert back to polar)
A= 150∠60°, B= 100∠135°, C= 150∠260°
3. Given an electronic circuit with an inductor and a resistor in series. The inductor has a value of XL= 100 Ω and the resistor is R = 120 Ω what would the total opposition be in the circuit in polar form if the total opposition is 120 Ω + j100 Ω?
4. If a rotor has run counterclockwise to the rectangular coordinates (−4, −4). Through how many degrees has it passed if it started at 0°?
5. A crank 189mm long, starting 200 from the origin (lead) turns in a counterclockwise direction 750. What is the horizontal projection of the line at the end point?
6. You have a circuit with a combined R value of 1.2 kΩ + j3.1kΩ. The voltage you are supplying has a value of 16 V ∠ 0°. Find the current in mA in the circuit using ohms law (V=I*R). Be sure to include the angle