Complex Plane and Transformations Quiz

A coordinate system where each point is represented by a complex number of the form a + bi, where 'a' is the real part and 'b' is the imaginary part.

A rotation of an angle π/3 radians around the origin O in the complex plane.

A rotation of an angle π/5 radians around the origin O in the complex plane.

The set of all ordered pairs (x, y) that satisfy the equation 3y = 5(15 - x).

The point on the unit circle (circle with radius 1) in the complex plane.

The distance traveled by point A along the unit circle after undergoing p rotations r₁ and q rotations r₂.

A dilation or resizing of the complex plane with a center O and a scale factor of 4.

A dilation or resizing of the complex plane with a center O and a scale factor of -6.

A combination of a rotation r₁ and a homothety h₁, represented as r₁oh₁.

A combination of a rotation r₂ and a homothety h₂, represented as r₂oh₂.

A repeated application of the similarity s₁ for 'm' times, expressed as s₁∘s₁∘...∘s₁.

A repeated application of the similarity s₂ for 'n' times, expressed as s₂∘s₂∘...∘s₂.

A combination of the composition sm and sn, expressed as sm∘sn.

A transformation that preserves shape and orientation while changing size.

The center point of the similarity transformation, where all points are mapped proportionally.

The scaling factor of a similarity transformation.

The angle of rotation in a similarity transformation.

The transformation 'f' is a direct similarity with a center O, a ratio of 22m x 3-3n, and an angle of mπ/3 + nπ/5.

The transformation 'f' is a direct similarity because it preserves shape and orientation while changing size.