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.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12