"

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

 

Unit 7.5 Printable Copy

License

ESET1140: Intermediate Technical Algebra Copyright © 2024 by froenico. All Rights Reserved.