Question

Let z = z = 8 (cosine (StartFraction pi Over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) ) and w = 3 (cosine (StartFraction pi Over 6 EndFraction) + I sine (StartFraction pi Over 6 EndFraction) ).

Which statement describes the geometric construction of the product zw on the complex plane?

Stretch z by a factor of 3 and rotate StartFraction pi Over 2 EndFraction radians counterclockwise.
Stretch z by a factor of 3 and rotate StartFraction pi Over 6 EndFraction radians counterclockwise.
Stretch z by a factor of 24 and rotate StartFraction pi Over 2 EndFraction radians counterclockwise.
Stretch z by a factor of 24 and rotate StartFraction pi Over 6 EndFraction radians counterclockwise.

Answer 1

The geometric construction of the product zw on the complex plane is to stretch z by a factor of 24 and rotate π/2 radians counterclockwise.

Step-by-step explanation:

To find the geometric construction of the product zw on the complex plane, we need to multiply the magnitudes and add the angles of z and w.

Given that z = 8 (cos(π/3) + i sin(π/3)) and w = 3 (cos(π/6) + i sin(π/6)),

The product zw = 24 (cos(π/3 + π/6) + i sin(π/3 + π/6))

Simplifying the angles, we get zw = 24 (cos(π/2) + i sin(π/2))

This means the geometric construction of the product zw on the complex plane is to stretch z by a factor of 24 and rotate π/2 radians counterclockwise.

Answer 2

(B) Stretch z by a factor of 3 and rotate π/6 radians counterclockwise.

Step-by-step explanation:

edge:2022 Happy new year!