Question

What is the quotient of the expression 90(cos(π/4) + i sin(π/4)) divided by 2(cos(π/12) + i sin(π/12))?

Options:
A. 45(cos(π/6) + i sin(π/6))
B. 15(cos(π/3) + i sin(π/3))
C. 30(cos(π/6) + i sin(π/6))
D. 45(cos(π/12) + i sin(π/12))

Answer 1

The quotient of the given complex numbers in polar form is found by dividing the magnitudes and subtracting the angles. The correct solution is 45(cos(π/6) + i sin(π/6)), which corresponds to option A.

Step-by-step explanation:

The student is asking to find the quotient of the complex numbers 90(cos(π/4) + i sin(π/4)) divided by 2(cos(π/12) + i sin(π/12)). To solve this, we use the properties of complex numbers in polar form where the division of two complex numbers requires dividing their magnitudes and subtracting their angles.

First, we divide the magnitudes: 90/2 = 45. Next, we subtract the angles in the complex number expressions: (π/4) - (π/12) = (3π/12) - (π/12) = (2π/12) = π/6. Therefore, the expression simplifies to 45(cos(π/6) + i sin(π/6)), making option A the correct answer.