Question

40cis60°(5cis60°) convert to rectangular.

a) 20 + 20i√3
b) 20 - 20i√3
c) 20i√3 - 20
d) 20i√3 + 20

Answer 1

To convert the complex number 40cis60°(5cis60°) to rectangular form, we can use the formula r(cosθ + isinθ), where r is the magnitude and θ is the angle. The correct answer is c) -100 + 200√3i.

Step-by-step explanation:

To convert the complex number 40cis60°(5cis60°) to rectangular form, we can use the formula r(cosθ + isinθ), where r is the magnitude and θ is the angle. In this case, we have:

r = 40 * 5 = 200

θ = 60° + 60° = 120°

Now, we can convert to rectangular form:

Real part: 200 * cos(120°) = -100

Imaginary part: 200 * sin(120°) = 200√3

Therefore, the correct answer is: c) -100 + 200√3i