Question

The product of (3+4j)(1−2j) in polar form is Select one:

a. 3.68∠+43.3∘
b. 3.68∠−62.4∘
c. 5.39∠−158∘
d. 5.39∠−21.8∘
e. 11.18∠+169.7∘
f. 11.18∠−10.3∘
g. none of the above

Answer 1

The product of (3+4j)(1−2j) in polar form is 11.18∠−10.3° or 11.18∠+349.7°, which corresponds to option (f). This is computed by multiplying the magnitudes and adding the angles of both complex numbers.

Step-by-step explanation:

The student has asked for the product of two complex numbers in polar form. To find the polar form of the product of (3+4j)(1−2j), we need to multiply the magnitudes and add the angles of the two complex numbers. First, let's find the magnitude and angle of each complex number.

• The magnitude of 3+4j is √(3² + 4²) = 5.
• The angle of 3+4j is arctan(4/3), which is approximately 53.1°.
• The magnitude of 1−2j is √(1² + (-2)²) = √5.
• The angle of 1−2j is arctan(-2/1), which is approximately -63.4° (adding 360° if you want a positive angle).

Multiplying the magnitudes gives us 5 * √5, and adding the angles gives us 53.1° - 63.4°. Thus, the product in polar form is 5*√5 at an angle of -10.3° or 349.7° (adding 360° to the negative angle).

In standard polar form, it can be stated as: 11.18∠−10.3° which corresponds to option (f).