Question

Multiply the complex numbers 3(cos(0.3) + i sin(0.3)) and 2(cos(0.2) + i sin(0.2)).

a) 6(cos(0.5) + i sin(0.5))
b) 6(cos(0.1) + i sin(0.1))
c) 5(cos(0.6) + i sin(0.6))
d) 5(cos(0.4) + i sin(0.4))

Answer 1

To find the product of two complex numbers in polar form, multiply their magnitudes and add their angles. The correct answer is 6(cos(0.5) + i sin(0.5)), which aligns with option a.

Step-by-step explanation:

To multiply complex numbers in polar form, you multiply their magnitudes and add their angles. The given complex numbers are 3(cos(0.3) + i sin(0.3)) and 2(cos(0.2) + i sin(0.2)).

Step 1: Multiply the magnitudes: 3 × 2 = 6.

Step 2: Add the angles: 0.3 + 0.2 = 0.5.

Thus, the product is 6(cos(0.5) + i sin(0.5)). This corresponds to option a in the provided choices.