Question

Find the product 4 cis (120∘)⋅5 cis (30∘)

A) 20 cis (150∘)
B) 20 cis (90∘)
C) 20 cis (60∘)
D) 20 cis (45∘)

Answer 1

To calculate the product of the complex numbers in polar form, 4 cis (120°) and 5 cis (30°), multiply the magnitudes and add the angles, resulting in 20 cis (150°).

Step-by-step explanation:

The subject of this question is how to multiply complex numbers in polar form. The operation involves finding the product of 4 cis (120°) and 5 cis (30°). When you multiply complex numbers in polar form, you multiply their magnitudes and add their angles. The magnitudes here are 4 and 5, and the angles are 120° and 30°. Multiplying the magnitudes gives us 20. Adding the angles gives us 150°. Therefore, the product is 20 cis (150°). Hence, the correct answer is A) 20 cis (150°)